Well, not exactly assassinate them or anything. You can join one side then do the Jagged Crown quest. You can give the crown to the other side and join them, betraying the side you took your oath for. I'm joining the Stormcloaks with my Dunmer just to betray them and do a little of their questline, can't imagine actually joining them with any character but a Nord.
I cant seem to find any reason not to join the Stormcloaks. The people are fighting for there home, their land! And my Argonian mage is going to help them.
On my second play through, I think I'll be a Nord powerhouse and join the Legion, just because I'm evil.