Oooh, me first!
Since they stopped playing Only Problem, which I still get stuck in my head from time to time, my answer would have to be Stretch Armstrong, I've always liked songs with a nightmarish quality to them (eg. Lullaby by the Cure), and I particularly liked the frenetic instrumental break. Before they changed it to 4/4, that is. Still an awesome song, but the instrumental break made it kinda unique. Or maybe that's my fondness for odd time signatures showing through. :)
Of the 'newer' songs, it'd have to be Elevators. When their album comes out, that song is gonna own the radio.
Ok, I've shown you mine, now show me yours! ;)