Asari, bar none. Were my favourite even before started playing MP, have become more favourite since
Liara is and will stay my favourite NPC of the trilogy.
I liked the geth ever since Legion's introduction. And yeah, the third game may have screwed a little with giving them the Pinocchio complex, but it actually made me like them more. Once again, I started liking them even more since I started dabbling in multiplayer.
Was pretty indifferent to drell before multiplayer, but the adept and vanguard changed that for me as well. If the entire race is as badass as those two, they have to be pretty damn cool.
Turians, because Garrus. Once again, MP and the fat turians only helped to reenforce that. Especially the fat Tsent 
I like Wrex, Grunt and warlord. Other than that, I'm pretty indifferent to krogan.
Vorcha are fun and I kinda like them, but wouldn't put them amongst my favourite. The flaming cheese they have going for them certainly doesn't make me like them more. Still think that Shisk is one of the more hilarious guys out there
Kinda on the same boat with hanar.
So yeah, a lot of MP bias going on here. Given I haven't played SP campaign in more than a year, that's kinda understandable, I guess.