If you like The Postal Service, you may also like Ben Gibbard's (the singer in Postal Service) other band: Death Cab for Cutie. A lot of people use that stupid "emo" moniker for them, but I would argue that they're more of a good "alternative" band.

I didn't see Coldplay listed in the comments for the last post, but that's some great stuff right there. I don't know too many people who don't like Coldplay. Check out Yellow off Parachutes or The Scientist off Rush Of Blood To The Head.

Dashboard Confessional's Vindicated is good. As is Hands Down.

The Shins' So Says I or Kissing the Lipless are good too.

Anyway. Those are just a few I can think of if you like The Postal Service.