Read somewhere that a lot of Americans sing Journey's 'Don't Stop Believin'. I personally find it an incredibly difficult song to sing.
Anyhow. Noraebang time!
I always start off with Jaurim's 'Hey, Hey, Hey'.
The music video is crappy; forgive it, it's old. I've been singing this for the past 12 years.
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Park Jinyoung 'Honey' (I think my noraebang self is stuck in 1997/1998.)
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Lexy 'Aesongi (Greenhorn)' (This one's pretty old, too.)
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And I always finish with Psy's 'Champion'.
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Oh, and Bohemian Rhapsody is mandatory for a group effort, because you inevitably wind up butchering it mercilessly. Hilarious.