You guys are thinking too much inside the box.
Yea, there's been teams that have tried to shape the world, end the world, and take over the universe. Honestly, I'm sick of that. Oh, and the repeated use of Zubat, Rattata, Koffing, and Ekans.
How about a team that seems nice, but actually has a drastically evil undertone?
Imagine this: said team--henceforth known as Team Alpha--is simply a small contributor to a large corporation, like Silph Co. Team Alpha helps to develop potions and other healing items sold in stores for Pokemon. No one knows it, but slowly and surely, Team Alpha is going to start making demands on the sales of their potions and, eventually, come out on top as a major corporate superpower because no other company has enough power to manufacture and compete with Team Alpha (Silph Co. makes electronics, not potions. Porygon, anyone?) This is happening as the protagonist goes undercover to figure out what is going on along with a team of individuals who helps him along the way (Team Beta). They learn what Team Alpha is up to, but it's too late and potions can no longer be bought elsewhere except from Team Alpha. This leads to many sick Pokemon and brings in a lot of money for Team Alpha. Realizing what is happening, the protagonist and Team Beta have to take down the corporation.
See? It's not about taking over the world. It's a corporation taking over an economy in a field that must not be messed with: medicine. With the potions and stuff under their control, it's not hard to see why they would succeed at this. Also, it adds an interesting gameplay element in that after a certain point, buying potions and such becomes really really hard, which means you need to battle smart and not die. =/
Just an idea. Those team names are just for simplicity reasons. I like the name GenCorp. :D