To start the community off, if I were stuck with nowhere else to go, it'd be mandatory for me to have Weezer's blue album in my possession. Anything with such melody automatically scores points in the "I really really really like it" category. By its side would likely be The Beatles' "Revolver," Queen's "A Night At The Opera" and Jamiroquai's "Travelling Without Moving" album. My music tastes are eclectic, but I'm willing to listen to anything as long as it isn't crappy bubble gum pop.
Go ahead and list your own musical preferences and start a revolution where we can share all our musical tastes, no matter how similar or different they may be!