Cool.
On the heavier side, there's the aptly-named Heavy, as well as Why, Pt. 2 (don't ask about part 1. I don't know what happened to it either. ) Precious Declaration is one of my personal favorites. On the grungier side, there's She Gathers Rain and Untitled Track.
Kinda in-between (rock-y, but not too heavy) is Shine, easily their most famous. Listen is a good one. There's also Him, AYTA, Hurricane, and December.
For some more mellow choices, we have Maybe, Compliment (live version's the best -- they performed with a full orchestra a few years back, and it's glorious), She Said, Needs, and The World I Know.
Hope I haven't gone too overboard. Let me know what you think! And no pressure to listen to every single one if you don't want to.