Pokémon Stadium 2
Pokémon Stadium 2 (ポケモンスタジアム2 Pokemonsutajiamu 2) is a stage for Super Smash Bros. Brawl, based on (as its name suggests) the Pokémon universe. The basic layout of the stage is essentially unchanged from Super Smash Bros. Melee's Pokémon Stadium, save for a major graphical upgrade, including a huge space between the crowd and the stadium. The name of this stadium might be a reference to the game Pokémon Stadium 2 for the Nintendo 64. As with the original Pokémon Stadium, every so often, the stage transforms to represent a certain Pokémon type (see "Elements" below). However, unlike its predecessor, Pokémon will occasionally appear in the background.
This stage is sometimes allowed as a counterpick in more liberal stagelists, but is usually banned in tournaments. This is because of many players see its transformations as heavily disruptive and too detrimental to gameplay; the electric transformation produces fast conveyor belts that easily push players off the stage and often result in self-destructs for less skilled/experienced players, the wind transformation significantly reduces gravity, which slows aerial approaches and results in earlier vertical KOs, and the ice transformation creates slippery terrain which alters how one must move on the stage as well as slightly increasing the chance to trip. Additionally, like PS1, all its transformation except for ice are susceptible to camping (though to a lesser degree than PS1).
However, PS2's legality has been heavily debated, with some players vouching for it and arguing its transformations to not be as disruptive as commonly claimed. They point out that self-destructs on the electric stage are due to player error and are avoided by players who properly play the stage, while also arguing that players who can't handle the conveyor belts can easily plank for the duration of the transformation (which is pointed out to not be functionally different than camping out a transformation on PS1 as is what commonly happens there). With the wind stage, they argue that while a stage that was permanently like that would be too detrimental for gameplay, for being there a mere 30 seconds (or minute) of the match its effect is too minor to warrant banning the whole stage, and that a sufficiently experienced player will never lose to a lesser skilled player because of it (this is additionally argued for the electric stage). With the ice transformation, it's argued that its effect is actually beneficial on gameplay, as the boosted speed and slide distance of DACUSes and slide smashes, the ability to slide with other attacks, and the increased sliding distance when shielding (which makes it more difficult to punish out of shield), allows the defensively-inclined Brawl to be played more offensively. PS2 supporters additionally point out that PS2 is arguably the most neutral stage in Brawl, where few characters, if any, gain a real advantage/disadvantage from the stage, as its very neutral standard stage and highly varying transformations neutralises advantages/disadvantages characters may have on the stage.
Despite the arguments of its supporters, the majority of players refuse to touch the stage regardless, and thus it is often banned outside liberal stagelists.
There are four possible stage transformations, each of which represents a particular type from the Pokémon games. While this feature was in the Melee version as well, the types represented in Brawl are all new. Whenever the stage transforms, the layout of its platforms changes, and in some cases the very physics of the game becomes altered as well. There is no specific order that these elements appear in - the stage transformation is completely random and it is even possible for the stadium to change into the same type twice in a row. However, the stage always begins on the standard arena and has to revert back to its normal state before transforming again. The elements are as follows:
A new feature in Pokémon Stadium 2 is the guest Pokémon who appear in the background of altered stages. They have no effect on the battle itself, but provide a nice addition to the scenery.
In the Stadium's Ice mode, there is a cabin in the middle of the stage. Hidden in the cabin is a poster of a kitten as well as what looks like the Wii Hint Cat on the same poster. It is unknown whose kitten is pictured on the poster, but it was rumored to be Masahiro Sakurai's. However, Sakurai later stated on Twitter that this is not the case. 
A stage such as this has never been seen in any main series Pokémon game. However, just like Pokémon Stadium, it looks identical to the arenas from the Pokémon Stadium games. The arenas in Pokémon Stadium have the Poké Ball logo in the center with crowds watching the battle, and the various arenas in the game were heavily aesthetically themed (such as the ice type gym being covered in ice), just like the type specific transformations of this stage.
While the other transformations don't seem to have a specific origin, the flying transformation's aesthetics are reminiscent of Valley Windworks from the Sinnoh region. The transformation features wind turbines like those seen in Valley Windworks, and the rare Pokémon Drifloon makes a guest appearance here, where in Diamond/Pearl/Platinum, the Valley Windworks was the only location where a Drifloon could be encountered.