I think I've found a terrific story seed generator - the Duty Officer assignments on Star Trek: Online. There are dozens of potential adventures here, from relocating colonists to entertaining foreign dignitaries right through to investigating biogenic weapons and even officer evaluations (which would be a fun side-plot).
The ST:O Wiki has a listing (which will probably increase), and I'm fairly certain there'll be other types of assignments pop up as well (sector vs. shipboard, etc).
I'll keep an eye on it and post any updates that appear.
http://www.stowiki.org/Category:Sector_assignments
http://www.stowiki.org/Category:Shipboard_assignments