When batteling with people via the random matchup, some Pokemon will always be banned. These are Mewtwo, Mew, Lugia, Ho-Oh, Celebi, Kyogre, Groudon, Rayquaza, Jirachi, Deoxys, Dialga,Palkia, Giratina, Phione, Manaphy, Darkrai, Shaymin, Arceus, Victini, Reshiram, Zekrom, Kyurem, Keldeo, Meloetta and Genesect.
All other legendaries, like the Bird Trio and the Lake Trio, can be used.
However, if you set up a battle with a friend using friend codes, you can use all Pokemon, including those I just mentioned.
Also, some tournaments allow you to use all Pokemon, but by default they cannot be used.