I am a music composer. Where can I find a place to host my MIDI and BAM files?

You can upload your music to this wiki and link to it on the Free Music page. Music must be a suitable free license like public domain or creative-commons or GPL if you want to upload it to this wiki.

You can host your music on Slime Salad and tag it appropriately ('resources', 'free music', etc).

Castle Paradox also allows users to host their own music files and let others browse through them. You can upload your music as any or all of (including multiple versions in different formats) BAM, MIDI, OGG, WAV and MP3, and rate people's music.

Apart from that, a lot of the time your ISP will give you some free webspace, you could put them there.