Song without drums here -> minusDrums - redirect
We have 282 original and cover songs without drums. The covers are both old and new so plenty of variety (about 60 tracks).
As far as what they are called... I personally call them drumless tracks, but if you google stuff like "songs without drums" or "drumless music" you'll find a bunch of stuff on the internet.
Be careful as a lot of the material out there is copyrighted material ripped from Rock Band and stuff. Some of the material is pretty crappy midi, but there are some guys out there making some great stuff for free, as well.
Anyway, I hope you stop by and see if we have something you like. You do get a free track when you register at the site, so you'll be able to add at least one track to your hopefully growing catalog.