Yes, but only in the main series, and there is some falsity to that
From Red and Blue to Black and White Two, there have been five villainous teams, Rocket, Magma, Aqua, Galactic, and Plasma, with Flare being the newest one in the upcoming X and Y. Aqua and Magma are the only one's to appear as primary antagonists side by side. However, in Black and White 2, Team Plasma is split into two opposing factions, so it could be argued there are two villains there as well, but it is really only one of the factions (Ghetsis' faction) that is evil, with the other faction (N's faction), actually helping you along the way.
However in the side games, teams do appear together. Team Snagem and Cipher were both in Pokemon Collesseum for example. In addition, in XD: Gale of Darkness there are multiple teams, including Cipher and an offshoot of it called Team Miror B., but only the former poses a significant threat. I may have missed some examples.
Hope this helps