OUYA $99 - no remote, comes with a controller though, and you'll have to mess with it, side load xbmc/xmbc ports/etc
Pi - Already covered
Intel NUC - you can get a celeron one for cheaper than the i3 listed, or the new bay trail one seems to be shipping. They are all barebones, so you'll need to buy RAM, and either a hdd/mSATA drive, or use a fast flash drive and something like OpenELEC. Still more than $100 ($200 is more accurate i'd say) but at least it's just a tiny PC with options, as opposed to some of the other android based options, etc.
You can probably still find a lenovo Q190, but thats an entire PC, ready to go (includes ram/hdd/etc) and at least $300 i think.
You can use the celeron/mb combo
here, and just build it into a case you like, add as much or as little, etc and be done. I think a NUC is cleaner though