Walk around the ship in between missions to hear some funny quotes:
Stand near Jeff "Joker" Moreau (the pilot) without interacting with him. You will hear him say things such as the following:
"Why is it always claws and guns? Can't we piss off a fuzzy planet? Still dangerous, I know. But hey, bunnies." "Two years and everything hits the crapper. That'll teach you to die on me." "You know what I hate about deep space? Crap radio stations from two centuries back. My gosh, we were idiots."
Stand next to the two engineers near the Mass Effect Core to hear the the following:
Engineer Daniels: "Did you know we're sharing our deck with a krogan?" Engineer Donnelly: "Well that's just peachy."