One thing I've loved about the Mass Effect universe, is that it made me care about the individual characters, along with the races and governments as a whole. Seriously, not even Star Wars could do that for me, and they have Wookies!
But to answer your question, probably the Quarians. Just because they're a very interesting nomadic race, and they're a lot tougher than they let on. Seriously, they're forced to constantly move around the galaxy, go through hardships just to keep their homes up and running, and they can die from a friggin cough! Sure, it's mostly their fault they ended up this way, but that doesn't discount the amount of badassery they have achieved.
Close second are the Turians. They're calculating, militaristic, they sound cool, and asskick runs in their blood.