Stuff I like:
Death Cab for Cutie–I Will Follow You Into the Dark
Desaparecidos–The Happiest Place on Earth
Fiona Apple–Extraordinary Machine
These are all uploaded onto various sites (I found them through a website that has a bunch of mp3s uploaded, so if you’re interested in a certain song or band, you can listen to it and decide if you like it, without downloading it onto your computer.) and they’re in mp3 format, so it should work on most browsers. 
