Well there's the classics like the Ramones, The Clash, Iggy Pop and The Stooges, those kinds of bands.
If you're into newer rock stuff there are a bunch of great indie bands like the Shins, The Von Bondies, the Strokes, Cinemechanica (these guys !@#$% rock), Death Cab For Cutie, etc
If you're looking for softer, kinda folkish music there's tons of great artists like Damien Rice, Elliott Smith, Iron and Wine, Flight of the Conchords (comedy folk :]), and the various Saddle Creek signed bands.
And of course there's the good techno/hip hop stuff like Frou Frou, Familjen, Uffie, and Lady Sovereign (I'm not sure if I spelled that correctly :/)
Any ways just a few suggestions. If you do change your mind about metal I have about a million great bands to recommend. Even still you should check out Protest the Hero. There kind of like punkish/rockish with Coheed and Cambria-ish vocals over sick prog metal guitar shredding. Not your typical bree bree growl brutal hardcore metal stuff, very melodic instead :]