The Advanced Linux Sound Architecture provides audio interface device support and an audio / MIDI API:
http://www.alsa-project.org/
Jack is a low-latency audio server. It allows connections inbetween applications and to devices:
http://jackaudio.org
The Linux Audio Developer's Simple Plugin API:
http://www.ladspa.org
An API aimed at synthesis plugins:
http://dssi.sourceforge.net
LADSPA Version 2:
http://lv2plug.in
Session management for Jack and ALSA applications:
http://www.nongnu.org/lash/