Nightcore is music that is speeded up and has a higher pitch than normal in order to produce a more happy effect.
Check out the examples below. They're all really good.
Examples:
Techno Nightcore
http://www.youtube.com/watch?v=9G9iilo-_oY (http://www.youtube.com/watch?v=9G9iilo-_oY)
http://www.youtube.com/watch?v=C-5YFRMLokk (http://www.youtube.com/watch?v=C-5YFRMLokk)
http://www.youtube.com/watch?v=6pvLlkCnExo (http://www.youtube.com/watch?v=6pvLlkCnExo)
http://www.youtube.com/watch?v=9opk1Lxwb1Y (http://www.youtube.com/watch?v=9opk1Lxwb1Y)
Hip Hop Nightcore (Gotta love the bass in rap/hip hop nightcore) :)
http://www.youtube.com/watch?v=MSwYaDIFlXw (http://www.youtube.com/watch?v=MSwYaDIFlXw)
http://www.youtube.com/watch?v=gmuhspFq4iM (http://www.youtube.com/watch?v=gmuhspFq4iM)
http://www.youtube.com/watch?v=OpuRQacNqF4 (http://www.youtube.com/watch?v=OpuRQacNqF4)
http://www.youtube.com/watch?v=jr7Es24mmU8 (http://www.youtube.com/watch?v=jr7Es24mmU8) (This one is really good)
Rock Nightcore
http://www.youtube.com/watch?v=vfMsZJ67n3c (http://www.youtube.com/watch?v=vfMsZJ67n3c) (I'm sure you've heard the original song)
http://www.youtube.com/watch?v=FyWIAz4_wzk (http://www.youtube.com/watch?v=FyWIAz4_wzk) (I wonder if this song is suitable for the Fanime rave)
http://www.youtube.com/watch?v=w1Fxxrj8zW0 (http://www.youtube.com/watch?v=w1Fxxrj8zW0) (Should be familiar if you play Guitar Hero)
http://www.youtube.com/watch?v=N-t7_IhAah8 (http://www.youtube.com/watch?v=N-t7_IhAah8) (This one makes you want to get up)
Michael Jackson Nightcore
http://www.youtube.com/watch?v=S0Rt55JE-Ns (http://www.youtube.com/watch?v=S0Rt55JE-Ns)
http://www.youtube.com/watch?v=RrRcOymUbk4 (http://www.youtube.com/watch?v=RrRcOymUbk4)