Strength Equals Worthiness

Suppose there's some great powerful being that you want on your side. It might be some magical or elemental creature, someone who's a really great fighter, or maybe something that you can summon. You seek it out and try to convince it to help you. Its reply? "You must first prove your worthiness by besting me in physical combat!"

Can be (somewhat) justified if Tell Me How You Fight is involved.

See also Asskicking Equals Authority, Might Makes Right. Related to Violence Is the Only Option and Sister Trope to Defeat Means Friendship.

Anime and Manga

 * Subverted in Fairy Tail, where the person is someone other than the one fighting. Elfman requires that anyone who wants to date his sister be capable of besting him physically, without magic.
 * In Ginga E Kickoff, Erika challenges Shou to a heading contest for the right to recruit her into his budding soccer team.

Mythology/Folklore

 * Atalanta of Greek Mythology, who would only marry a man if he could best her in a foot race.

Video Games

 * Final Fantasy. If you want to use Summon Magic, chances are you're going to have to fight the creature first -- and they'll probably say something along the lines of "you need to prove your strength/worth!" too.
 * Both subverted and played straight in Final Fantasy VIII, as you have to draw most of the summons from bosses - and not the actual summons themselves. There are a few summons where this trope is played straight, though.
 * Subverted in Tales of Phantasia; The first five summons need to be fought before they'll join you, but when the party gets to Luna, they're ready to have a match with her ("We don't mind if you want to test our strength!") but she decides to simply join them without a fight.
 * Also justified with Volt, who had gone berserk. Once you beat him into submission he calms down and becomes lucid again. (to a degree)
 * The Divine Danans in Treasure of the Rudra need to be defeated to "prove you're worthy of their knowledge".
 * Justified with, who is already willing to ally with you, but in this case strength is a big deal, since they want to know if you're strong enough to defeat the Big Bad.
 * Very annoyingly happens in Grand Theft Auto: Vice City. You have to beat the infuriatingly skilled Hilary in a difficult race before he'll agree to be the getaway driver for your bank job. Not only is this mission possibly the hardest in the game, but Fridge Logic dictates that if you could beat him then you wouldn't need him to be your driver in the first place. Of course, none of that matters, because he dies during the job and you have to drive the getaway car anyway.
 * In Twilight Princess, the Gorons have become something of a Proud Warrior Race, and equate physical strength with strength of character. Therefore, they refuse to let you help until you beat them in a sumo match (which you win by cheating).
 * The Barbarian Elders on Mount Arreat in Diablo II: Lord of Destruction.
 * Pretty much the entire premise of unlocking characters in the Super Smash Bros. (though, in Brawl, many are unlocked as you play through the campaign mode).
 * The Boreas Seabed mission in Guild Wars Factions.
 * Star Ocean likes to rub your face in this trope. You have a set of trials to pass, including the Power and Courage trials. Power Trial? Defeat a boss, fair enough. Courage trial? Defeat a boss, to prove you have the power to back your courage! What the...
 * Yes, Power: The RPG universe's gold standard since 1986.
 * The exact same boss, at that...
 * In Yakuza 3, to use certain weapons you need a certificate, which you earn by defeating your weapons master while he, not you, is using said weapon.
 * The guardians of the elemental crystals in MARDEK refuse to give you the crystals until you best them in physical combat. Surprisingly, this is is not lampshaded even once!
 * In The Reconstruction, assumes this when he is told he will be put through a "test" by a mysterious stranger; he quickly objects, but it turns out the test is of a different nature.
 * Catching Pokémon is based on this principle.
 * The Guardians in Solatorobo operate on this principle, telling Red that if he can't solve their riddles, he must beat them in combat instead. Red, being Red, chooses to fight.

Web Comics

 * As a JRPG Homage, Aetheria Epics features this as well (to gain the more powerful summons, Allete has to beat them in battle).