Apparently Dawn of War 2 has co-op campaigns, as does Red Alert 3. I have not played either one of those, though.
Co-op in RTS generally means playing skirmish against the AI. Games that my group has played and really liked for co-op:
Age of Empires I-III
Empire Earth (the sequels were not as impressive)
Empires: Dawn of the Modern World
Rise of Nations (Rise of Legends was okay, but not our fav)
Supreme Commander and Forged Alliance (for the best AI, use Sorian's AI mod, but it is a bit slow)
Civilization IV
Of all of those, AoEIII and FA were probably our favorites. These are all wonderful games, and we got at least 6 months if not more like a year or more of play out of each. However, the ongoing frustration was that after we got to a certain level of skill, the AI was just no match for us. Plus, a lot of the more recent games don't allow multiplayer saves for some reason, which is a real problem for co-op (most of the earlier games, like AoE2 and Empire Earth, do have this feature).
Anyway, so there are a lot of good options up there on that list, and that other people have mentioned all throughout this thread. To add one more, you might try out the cooperative-focused RTS game that I created myself, AI War: Fleet Command (link:
http://www.arcengames.com/). I got tired of waiting around for the bigger developers to focus more on cooperative play (the opposite trend seems to be present instead), so I created a game myself. The demo is free, and you can play with up to 8 players against 2 very challenging AIs (which you can tone down the difficulty on with ease). Hopefully you like it -- most people seem to so far, but it's early yet -- but otherwise give the list above a try. There are cooperative RTS games out there, but they are few and far between even now.