Stock Ninja Weaponry

Ninjas are cool, whenever they appear. They're masters of stealth and deception and use exotic moves and techniques to trick their opponents. Part of their coolness tends to come from their weaponry, which is usually used to make their role more obvious. See a certain weapon in the hands of a warrior usually gives away his identity as a ninja. Said weapons usually are:

Shinobigatana or Ninjato: The ninja sword, similar to a short, straight katana, and usually held in Reverse Grip. Sometimes Wakizashi or Tanto (Shortswords and Daggers) are used instead.
Kunai: The throwing daggers, created from gardening tools. They're usually thrown en masse or used for a Knife Outline.
Shuriken: Probably the most popular and recognizable ninja weapon. Like the above mentioned Kunai, they're usually thrown in great numbers. In case of Highly-Visible Ninja expect to see the Fuuma Shuriken.
Kusarigama or Gama: Small scythes, especially when attached to an Epic Flail tends to be a popular choice for ninja in fiction. However expect to see the user swinging the scythe around. Variations include the Okinawan Kusarigama, which has sickles on both ends.
Nunchaku: Often seen in the hand of ninja fighters for some reason.
Claws and Hidden Blades: Both of the Wolverine Claws and Blade Below the Shoulder variation are sometime seen. In Real Life, Ninjas did used a claw-like weapon called Neko-te but mainly for climbing.
Makibishi: Caltrops, often used while running away from a foe.
Nageteppo: Low-tech smoke and/or flash bombs.
Sai: Are often seen as weapons for Ninja.
Senbon or Needles of various size were used by ninjas. Some of them were big, while others were small enough to be carried in the mouth and then shot using the tongue as a blowpipe. Often Poisoned Weapons.
Manriki Kusari or Kusari Fundo: Chains with heavy weights to the ends, used for disarm people or entangle and trap them.

For more info, see The Other Wiki's page on it.

Examples of Stock Ninja Weaponry include:

Anime and Manga

Naruto has used almost all the above mentioned, being a series about ninjas, examples include: Kunai and Shuriken are used as the default weapon for many Ninjas, the ANBU use Ninjato, Sasuke has his Fuuma Shuriken and Gai can use Nunchaku in battle. Resurrected!Hanzo use a Kusarigama, and so did Madara Uchiha.
The Tamagakushi Ryuu from Gamaran employ shuriken, kunai and shortswords in battle.
Kotaro Fuuma from Yaiba use a lot of ninja weapons, including a Shinobigatana, kunai, shuriken and even a Kusarigama. Later Ishikawa Goemon is shown using kunai, smoke bombs and sai.
Sui Feng from Bleach is basically a Ninja, and at least once she use a volley of kunai in order to pin Ukitake to a tree (It Makes Sense in Context). Furthermore her Zanpakuto takes the form of a wakizashi when sealed, and a Blade Below the Shoulder weapon when released.
The one-shot villain Murasaki from Dragon Ball claims to be a Ninja. His weapons include a ninja sword and various knives amongst other things.
Tsubaki from Soul Eater isn't just proficent with "ninja" weapons; she transforms into them (more specifically she has smoke bomb, kusarigama, tanto, giant shuriken and katana forms). Her partner BlackStar wields her. Interestingly Black Star's mentor Sid (despite being ninja themed) averts this trope by specialising in knives (his partner takes the form of a modern, Western survival knife).
There's one Lupin III episode where our heroes are challenged by a group of four ninjas and a kunoichi (actually a Villainous Crossdresser) who take a great pride in using old-school weapons, including swords, daggers and kusarigama. They also add axes and bows to the lot.
In Basilisk many characters employ kunai daggers and tanto. We also have Gennosuke and Tenzen (katana), Nenki (a long nunchaku that can turn back into a pole), Jubei (an Aikuchi dagger hidden in his esophagus), Koshiro (two kama) and also Danjo Koga (needles).

Comic Books

Teenage Mutant Ninja Turtles: the titular characters are armed with Ninja weapons, plus a Bo staff.

Literature

In James Clavell's Shogun the shinobi aiming at Mariko's life are described wielding poison-covered shurikens, swords and "scythe-like knives connected to long weighted chains" (aka: Kusarigama).

Live Action Television

Ninja Sentai Kakuranger: Shuriken show up, wielded by all of the rangers. Most are of them are small. Each ranger has unique shuriken which resemble their ranger symbol. NinjaRed also has a Fuuma Shuriken, with his first Humongous Mecha wielding a bigger version that it rolls at enemies to kill them. The rangers also Caltrops on a few occasions. Each of them has a wakizashi in Ranger form, and finally NinjaRed's third Humongous Mecha wields a pair of ninja-to.

Tabletop RPG

Dungeons & Dragons Oriental Adventures supplement (1985) gave the following as ninja weapons. Some are already in the trope description and are not repeated here.
- Kawanaga. A length of rope with a grappling hook at one end and a hook on the other. Used for climbing walls and in combat to damage or entangle an opponent. The Other Wiki has this as Kaginawa.
- Kumade. A long wooden shaft with a rake head at one end. Used to climb walls or attack others in combat.
- Kyoketsu-shogi (AKA Kyoketsuogi). Similar to the Kawanaga, but with an sharp hooked blade at one end and a heavy iron ring at the other. Can be swung to strike with the blade or ring, to entangle an opponent or be thrown like a bola. According to The Other Wiki it's spelled Kyoketsu-shoge.
- Needle. Held in the mouth and either spat at or blown at (using the tongue as a blowpipe) an opponent at close range.

Video Games

In Shinobido Goh can use a Ninjato and also shuriken, makibishi and smoke bombs.
Sengoku Basara has the three main ninjas (Sasuke, Kasuga and Kotaro) using appropriate Ninja weapons, namely a Fuuma Shuriken, kunai and a couple of Ninjato.
In Samurai Warriors Hattori Hanzo wields a Kusarigama in battle. Other ninjas include Kunoichi and Nene (daggers) and Kotaro Fuuma (clawed gauntlets).
In Samurai Shodown both Hanzo and Galford wields Ninjato and can throw shuriken or kunai, while Earthquake uses a massive Kusarigama.
Ryuu from Ninja Gaiden, whose massive arsenal includes some ninja-related weapons.
In Onimusha ninja characters like Kaede and Kotaro Fuuma are armed with kunai-like daggers and can use shuriken as distance weapons.
In The Adventures of Willy Beamish of all people the terribly stereotipical Japanese tourists will give you a smoke bomb and a shuriken as a gift. It's later revealed that they actually are ninja in disguise.

Western Animation

In a late episode from The Simpsons the Comic Book Guy tries to win back his clients by offering them "Ninja Weapon" to buy. We get glimpses of katana, kusarigama and shuriken among other things.
The South Park episode "Good Times With Weapons" sees the boys buy ninja weapons and run amok with them.