Poké Ball

The Poké Ball (モンスターボール) is an item that if thrown, releases one of a number of Pokémon. Each Pokémon does a different thing, including attacking one's opponent, changing the properties of the stage, and inducing status effects. The Poké Balls in Super Smash Bros. release Pokémon from Pokémon Red/Blue/Yellow, while the Poké Balls in Super Smash Bros. Melee release Pokémon from Pokémon Gold/Silver/Crystal in addition to Pokémon from Red/Blue/Yellow. The Poké Balls in Super Smash Bros. Brawl release Pokémon from the first four generations, which include, along with past generation Pokémon, Pokémon from Ruby/Sapphire/Emerald, FireRed/LeafGreen, and Diamond/Pearl. In Brawl, the Poké Ball makes a unique sound effect when it appears, thus alerting one to its presence even if it appears off screen.

In Brawl, the number of Poké Balls that can be on-screen at once has been reduced to three, instead of the unlimited number of Poké Balls that could appear in Melee. In Training Mode in Melee, a numerous amount of Poké Balls may be taken out, however, some that are thrown may result into letting out no Pokémon at all.

The Poké Ball is also featured as a trophy in every game except for the original Super Smash Bros. on N64.

Pokémon in Super Smash Bros.
Super Smash Bros had 13 Pokémon:

Pokémon in Super Smash Bros. Melee
Super Smash Bros. Melee had 29 Pokémon (8 of them returning from Super Smash Bros.):

Pokémon in Super Smash Bros. Brawl
Super Smash Bros. Brawl had 31 Pokémon (16 of them are returning, all but 1 from Super Smash Bros. Melee):

Pokémon in Super Smash Bros. for Nintendo 3DS and Wii U
Super Smash Bros. for 3DS and Wii U introduced the Master Ball, a type of Poké Ball that will only release rare or Legendary Pokémon (although it may summon a Goldeen). There are 42 Pokémon that appear overall (19 of them are returning from Super Smash Bros. Brawl):

Trophy Info (Melee)
''These balls are used to capture and contain wild Pokémon. Most Pokémon must be weakened in some way before they can be captured, but once they're inside a Poké Ball, they enjoy their new home, since Poké Balls contain an environment specially designed for Pokémon comfort. Master Balls are the strongest type.''

Trophy Info (Brawl)
''An item used for capturing Pokémon and calling them out to battle. Pokémon live in these items which, despite appearances, actually contain a wide, comfortable, Pokémon-friendly world inside them. In Super Smash Bros., Pokémon give temporary support to whoever calls them out. You never know which Pokémon you'll get, but some of them are devastatingly powerful.''
 * Pokémon Red/Blue (1998)
 * Pokémon Diamond/Pearl (2007)

Trophy Info (Wii U/3DS)
''An item used to call out different Pokémon. Which Pokémon emerges is a mystery, but it will aid whoever threw the Poké Ball. Some of the Pokémon contained inside are extremely powerful and will really intensify the battle. It's definitely worth beating your opponents to these!''
 * Game Boy - Pokémon Red & Pokémon Blue (09/1998)
 * 3DS - Pokémon X & Pokémon Y (10/2013)

Trivia

 * CPUs in Super Smash Bros. Melee will pursue a Poké Ball, no matter how far, even if it means that the CPU must cease fighting. This is less common in Super Smash Bros. Brawl, but not by much.
 * The physics of the one who has a Poké Ball has changed between Melee and Brawl. In Melee, unless the Poké Ball is reflected, once a character picks up a Poké Ball, its Pokémon will definitely belong to the character. However, in Brawl, the Poké Ball can now be caught in midair. It also won't release the Pokémon inside if the character drops the Poké Ball via enemy attacks.
 * The first Pokémon summoned from a Poké Ball in Training Mode also becomes the first summoned in Versus Mode.