Kung Fu Wizard

In one corner, you have the Squishy Wizard, supernaturally adept, but physically an utter weakling. In the other stands the Kung Fu Wizard, who not only has supernatural powers, but is also a skilled martial artist. In fact, their martial arts practice facilitates the use of their powers, and may actually be the source of them. This character can use both Ki Attacks and Functional Magic, or blends them together until they're indistinguishable. The Kung Fu Wizard is most often found in Chinese folklore, Wuxia books and films, Manga, and Anime.

Sometimes they may overlap with Combat Medic. Because in real life, Monks were often religious figures and in fact, some of the Eastern monks did gain a reputation for knowing or developing Martial Arts. Thus, someone who practices Martial Arts may also know a few things about exorcism, healing, or dealing holy damage. Or Buffs.

See also Magic Knight, where the wizard is trained in weapon-based combat rather than martial arts, Supernatural Martial Arts, where the kung fu is itself magic, and Full Contact Magic, where the wizard doesn't actually know kung fu, but still needs to move around a lot to use magic. May be augmented via Meditation Powerup.

Anime and Manga
Additionally, while he has the ability to discharge electricity, he has to either be able to touch his target or have some sort of connection that will conduct electricity. (In other words, no lightning bolts) And "something that conducts electricity" includes the knives and choke wires he used anyway.
 * The Elric brothers of Fullmetal Alchemist are skilled martial artists as well as alchemists and this is also true of most State Alchemists. Edward is also able to transmute his arm to aid himself in combat.
 * And the brothers' trainer Izumi. Ed and Al are still scared of her.
 * Funnily enough, both this and her Training From Hell were explained in an Omake to have originated with her seeking an alchemist teacher who.
 * Justified with Hei in Darker Than Black -- the reason he's both a powerful Contractor and amazing martial artist (besides the fact he's Chinese) is that he started out as a Badass Normal and had to be strong enough to take on Contractors.
 * The very nature of combat in the Nasuverse demands that you have to be this trope if you want any of your hard-learnt spells to hit anything. Tohsaka Rin of Fate Stay Night and Kokuto Azaka of Kara no Kyoukai are equal parts deadly as magicians and warriors in their respective universes.
 * Of note though is that while they are fairly skilled in martial arts, they stand no chance in close combat with the more straightforward fighter-type characters. For example, Rin's athleticism helps her move around but her physical fighting abilities are completely worthless against anyone but Caster, who is very much the Squishy Wizard.
 * Louie of Rune Soldier Louie. Despite being the hero, he's terrible at both magic and swordsmanship, even though he was raised by the head of the mages guild, attended the mage academy for most of his life, and has trained in swordsmanship considerably with Genie. His only saving grace is that he is a very skilled brawler.
 * The titular character of Mahou Sensei Negima starts using just magic, but later on is told to make a choice between training for sheer magical power while lacking in straight-up fighting (thus needing a partner to protect while casting), or to balance magic and physical strength. He picks the latter, but instead of using weapons and magic like that person suggested, he instead learns martial arts from Ku Fei.
 * Really, at this point, this trope is practically the series' calling card.
 * In the festival arc Negi even shows up to fight in a tournament in a Wizard Robe with a martial arts gi underneath.
 * In Magical Girl Lyrical Nanoha ViVid, Vivio's fighting style is also a combination of martial arts and magic. She has as her martial arts trainer in ViVid while Nanoha-mama watches over her magic training.
 * Natsu of Fairy Tail is just as capable of beating you up as he is burning you to a crisp. Sometimes he'll do both at once.
 * In one early episode, a pair of professed Badass Normal mercenaries assume that all wizards are Squishy Wizards, recounting a story of a wizard who spent years mastering a curse that could break bones; they just broke his bones with a punch. As such, they were completely unprepared for Natsu's strength.
 * Gray as well. He gets a pretty badass moment where an enemy lures him into a trap that prevents Gray from using his ice magic without hampering the enemies' style of magic. The enemy gets a nasty surprise when Gray kicks him off his perch twenty feet in the air.
 * It's even more awesome when Gray does it to his senior pupil Leon. After deciding he has had enough, he manages to utterly overpower him using hand-to-hand combat even though Leon is the more experienced mage.
 * Many ninja in Naruto use a combination of taijutsu and less physical ninjutsu (some of which is more a case of Full Contact Magic), with some exceptions that focus on use of weapons or physical ability. One good examples is Chiyo who has both puppets and good hand-to-hand combat abilities.
 * Princess Amelia from The Slayers, proficient in martial arts, healing, and astral magic. Her father as well.

Comics

 * The various Immortal Weapons from Iron Fist are good Western examples of this.
 * Doctor Strange, master of the mystic -- and martial -- arts. On more than one occasion he has surprised enemies who expected him to be physically helpless without his magic.

Literature

 * Discworld's Mustrum Ridcully and Granny Weatherwax prefer crossbows or no physical fighting at all, respectively, but can still pummel the average villain or stop a sword blow with one bare hand. (Granny's also demonstrated the ability to make a wooden spoon as sharp as a sword.) Lu-Tze is a more conventional user of this trope; between martial arts and the ability to slice time finely enough to outrun lightning, there's a reason for Rule One: "Never act incautiously when confronted by a little bald wrinkly smiling man!"
 * Briar Moss, in Tamora Pierce's Circle of Magic series, wasn't exactly trained in martial arts, but he knows how to fight anyway from his life as a street rat.
 * In The Dresden Files, Harry (while not a full-blown Kung Fu Wizard) does take occasional lessons from Murphy. This combined with his great height (and thus reach), sprinter's build, long staff and willingness to fight dirty makes him pretty badass with what little martial art he knows.
 * Though the eponymous magic-users of Mistborn don't draw their magic from their fighting skills, said magic allows sufficient strengthening and controlling of body and mind to invoke the spirit of this trope, and per Word of God creating elaborate, martial arts-inspired fights was one of the author's goals in creating and using this power.

Live Action TV

 * Phoebe from Charmed is a Kung-Fu witch. Initially she's the only one with no active powers (her sisters can move objects and freeze things while she can see visions of the past and future) and took to learning martial arts. She eventually develops an active power, levitation, that is of great use in combination with her martial arts skills.

Movies

 * In Chinese Ghost Story, Yin and at least one other character. They show both martial arts and magic usually cast by throwing spells written on paper. This gets quite mixed, coming to a climax of fight choreography, flying around from tree to tree, and spellcasting.
 * The Korean film Woochi features several of these, most notably the titular character.

Tabletop Games

 * In Dungeons and Dragons, it's possible to create a multiclassed monk/wizard character. Horribly unoptimized like most builds involving multiclassing spell casters and taking levels in monk, but possible.
 * It is worth noting that Monk itself invokes a similar trope, its Ki Abilities eventually including teleportation and intangibility. Unfortunately these come far later than the wizard equivalents and have more limitations, besides not synergising with anything else.
 * In gestalt settings, Monk//Cleric and Monk//Psychic Warrior can be excellent choices, the first benefiting from the sheer number of offensive cleric spells that are in "touch" range.
 * The Tome of Battle supplement adds a few options which support this trope. The infamously poorly-worded Arcane Swordsage blurs the lines between this trope and Supernatural Martial Arts.
 * There are also feats that that make certain class combinations more viable. Ascetic Mage lets a Sorcerer/Monk (or Monk/Ex-Bard or Bard/Ex-Monk) add his spellcasting ability score to his armor class, Carmendine Monk lets a monk use his Intelligence instead of Wisdom for a lot of Monk abilities, including armor class (good for Wizards or Psions), and Tashalatora lets a character determine the power of certain Monk class features with the sum of his Monk levels and one psionic class (particularly good for Psychic Warriors and Ardents).
 * Prestige classes supporting this include Psionic Fist (monk/psionics), Enlightened Fist (monk/wizard users of Elemental Punch), Sacred Fist (monk/cleric) and Jade Phoenix Mage (swordsage/wizard specialising in fire). Anything which could be used to create a Magic Knight can also be applied to unarmed strikes.
 * Even if multiclassed or gestalt spellcasters aren't your thing, you can still make a single-classed spellcaster with the Improved Unarmed Strike feat, such as a grapplemancer-build wizard (Octopus familiar, enlarge spells), a Cleric (with magic weapon/greater magic weapon piled on a pair of gauntlets, and optionally the War domain), or a Druid (and magic fang/greater magic fang, although your Tiger's Claw technique may be quickly replaced with turning into an actual Tiger).
 * Pathfinder has the same basic options in this area as Dungeons and Dragons above, with different feats and prestige classes. In particular, a series of feats exists which allow a character to cast a specific spell/magical ability after hitting with an unarmed strike.
 * In Exalted, virtually any sorcerer character will be either this or a Magic Knight. It's technically possible to make a Squishy Wizard, but since the game world assumes a certain amount of combat ability for all characters, you're just making life difficult for yourself if you do, and the core rules themselves warn against this. And that's not even going into the various Supernatural Martial Arts And Crafts...
 * Anyone who can use magic in Hong Kong Action Theatre is probably going to be this, thanks to every character being proficient in both Gun Fu and some form of Kung Fu as well.
 * Dark Heresy mostly keeps its Psykers fairly squishy, making it harder for them to improve physical stats or learn combat skills. But then there's the Templar Calix career option, which lets you turn your wimpy freak into a mind-raping ninja assassin, dual-wielding psionically charged swords and specialising in hand-to-hand combat.
 * The Adamantine Arrow in Mage: The Awakening assumes this sort of person, being the security experts of the Awakened. The Perfected Adept takes it a step further.
 * The Akashic Brothers in Mage: The Ascension are this trope all over. They represent the tradition of bringing about enlightenment through the harmonizing of the body and mind. A side effect of this is that pretty much every single Akashic knows how to perform amazing stunts and kick serious ass, before they even whip out their reality warping powers.
 * Enlightened martial artists from Deadlands have the ability to tap into the energies of the Hunting Grounds, enabling them to leap tall buildings in a single bound and pluck bullets from the air, among other things.

Video Games

 * In the Dynasty Warriors series, many characters such as Sima Yi, Pang Tong, Zhang Jiao, etc. are literally squishy wizards who back up their magical attacks with martial arts prowess.
 * Final Fantasy V gives a monk magic commands for a very underbalanced version. You could also give the "Barehanded" ability to mages, allowing them to deal heavy damage with both attacks and magic.
 * Final Fantasy XII the Big Bad Vayne surprisingly fights this way beating you with his bare hands, throwing Ki Attacks, unblockable Last Disc Magic and a horde of magical swords at you.
 * Final Fantasy XIII gives us fighting with high speed martial arts and high powered Ruin spells.
 * Lightning can fulfill this trope as well when set as a Ravager, do to her utilizing various elemental sword strikes, while she is clearly a very proficient martial artist via various cut scenes and in actual in-game combat. In fact, she ties Vanille as the second most powerful mage/wizard/whatever in the party, and for martial strength is second only to Fang (who is the strongest out of all the party members).
 * An example of a Combat Medic meets the Kung Fu Magic are the monks and master monks in the Shining franchise. Shining Force gives us Gong, a monk who knows how to cast healing spells and can stand his own in combat. Then in Shining Force 2, monks can be made even more powerful to near Game Breaker levels. Sarah and Karna gain the Blast spell, so they can not only sends someone packing with their fists but can also inflict a little magic damage. The R Emake of Shining Force also allows Gong to attack with a wave of energy.
 * Ganondorf is frequently described as a "master wizard," but in the games themselves this power seems to be relegated specifically to fireballs, punching and kicking people to death while using dark energy to power up, swordplay, or turning into a beast to bite and claw victims.
 * Most of Ganon's magic isn't related to combat: he uses fireballs/energy blasts, he occasionally flies, but that's about it. He is very well-versed in large-scale barrier magic, summoning Phantoms, and cursing entire societies (freezing Zora's Domain seems to be a favorite).
 * Zelda. As a princess, she can deliver powerful magical blows; while as a ninja... You get the idea.
 * Vaati. In Minish Cap, he wins a sword fighting contest of people from around the world. In Japan, it was martial arts.
 * Dhaos from Tales of Phantasia is primarily a spellcaster, but will readily dish out a bare-handed beatdown to anyone who gets too close to him with his Tetra Assault arte. He gets an extremely powerful upgraded version of it called Million Assault in Tales Of VS.
 * Sync the Tempest from Tales of the Abyss is capable of casting several high level spells and Daathic fonic artes but spends most of the time pummeling you with his fists.
 * Rose from Street Fighter, a mystic who fights with Soul Power and her enchanted scarf.
 * Given the series' martial arts roots, Mortal Kombat's most powerful sorcerers, Shang Tsung and Quan Chi, are more than capable of kicking your ass with or without their magic.
 * In Dungeon Crawl, transmuters start with skill in unarmed combat and better physical stats than most other spell casting classes. This becomes especially useful when you get access to their shape shifting spells.
 * Xavier Pendragon from Eternal Champions might count as one, since he uses a combination of Hapkido Cane and alchemy in his fighting style.
 * Neverwinter Nights lets players mix-and-match multiple character classes, but the original campaign has a fine example of an Elvish Kung-Fu Wizard Pirate who shows up as an Elite Mook in Chapter 1, with very little explanation.
 * When she doesn't have a gun on hand, Jack's preferred mode of combat in Mass Effect 2 is to deliver biotic charges by punching people.
 * Thane, while lacking Jack's raw power, also combines hand-to-hand and biotics to lethal effect. His Shadow Broker dossier details examples of this technique, such as his standard method for neutralizing Asari targets.
 * Many Kingdom Hearts characters are Magic Knights, but the best example the series has of this particular trope No Heart, an optional boss fight with Master Xehanort's armor in Birth By Sleep: Final Mix. He could just hit you with his Keyblade, but why settle for that when he can morph into a piece of armour and punch / kick you with it?
 * Sveta in Golden Sun Dark Dawn is a beast-girl who fights with a martial-arts style, casts powerful wind and lightning Psynergy, and turns into a giant werewolf... who can still use martial arts and Psynergy. She punches bosses across the room. It is AWESOME.
 * Having been trained as a martial artist before becoming an Adept, it's reasonable to assume Feizhi grew up into one of these after Golden Sun.
 * Ivan's sister Hama trains the people of Xian in kung-fu, and Ivan and the aforementioned Feizhi in Psynergy, so this can be assumed of her, too.
 * For a villainous (maybe) example, Agatio in The Lost Age prefers bare fists to a weapon, but has the largest variety of Psynergy attacks among the Fire Clan antagonists.
 * Himika the red spirit in Eien no Aselia is unique for her class time because rather than being a squishy wizard, she's a straight up brawler who does best in melee. While she can work as a caster, her effectiveness declines quickly due to dropping Mind values.
 * Byakuren Hijiri from Touhou is said to be an example - while she is a proficient wielder of both holy and arcane magic, her specialty is said to be powerful body-manipulation she casts on herself to augment her physical prowess. Even in the games, where she is limited by the strict rules of spellcard duels and the realities of the genre, she shows a bit of this with her spellcard "Superhuman", which allows her to zip around the screen about as fast as Aya. Helps that she's a monk of the Kung Fu variety.
 * Hermana Larmo from Tales of Innocence can utilize magic of every element, but is more adept at punching out her enemies. The Vita remake narrows her magic down to a few buffing spells, further emphasizing her fists.

Web Comics

 * Four of the main cast members in El Goonish Shive practice "anime style martial arts", which looks like a Fighting Game with special effects even before it fades into generalized magic and serves as introductory magical training.
 * Richard of Looking for Group has unbelievably destructive magics at his command, but is also a very capable melee fighter who can even pull off a flawless Vulcan Nerve Pinch through armor. As he puts it: "I drained the soul of a monk once. It tasted like chocolate."
 * "I'm a bearlock now."
 * Ten Winds from Keychain of Creation could be considered this.

Web Original

 * In the Whateley Universe, Bladedancer is not only becoming a fearsome martial artist and user of Chi, but is also taking lessons in magic, and has used spell slips in fights.
 * Several of the fighters in Dead Fantasy, but Tifa is definitely the best example.

Western Animation

 * Nabu from Winx Club.
 * Uncle from Jackie Chan Adventures.
 * Practically all Benders from Avatar: The Last Airbender. They're each restricted to their own element (except for the Avatar, who can use them all), but they can either punch/kick you, hit you with their element, or both.
 * This is pretty much a required trope for all Benders as all bending is done through martial arts. Each element in Avatar The Last Airbender corresponds to a real martial art form and pro-bending in The Legend of Korra is essentially long-distance boxing.