There's an old game I grew up with called Castle of the Winds. You could also move using some other keys or the mouse, but for me my favorite way by far was using the numpad with numlock turned off.
I also used to use the numpad while playing Half-Life, as the person who introduced me to that game swore by remapping all the keys to the numpad.
Pretty much anything that let's you belt it out and really yell into the mic.
Most songs from Blink-182 are fun to sing.
+1 to Sweet Caroline by Neil Diamond, that's a classic.
I Guess That's Why They Call It The Blues by Elton John
Either Get Ready to Die or Party Hard by Andrew W.K.
Come to My Window by Melissa Etheridge if you can hit the high notes
Gompie's version of Who the X is Alice? If you have an audience that doesn't mind cursing and might have fun singing along.