Back when I sang karaoke on a regular basis, I would very frequently warm up with "Abacab" by Genesis. Other favorites were "New York State of Mind" by Billy Joel and "Don't Let the Sun Go Down On Me" by Elton John.
I rarely go out for karaoke now though, because especially since I quit drinking I don't like being in bars, and I much prefer singing and playing with live musicians.
I was partial to Alanis Morissette's "You Oughta Know," but that's only fun when drunk and/or pissed off. My non-intoxicated favorite is "Hot Patootie" from Rocky Horror Picture Show. My sing-with-a-group-of-friends favorite is the B-52s' "Love Shack."