The original Star Trek series had a lot of really neat sound effects, phasers, dematerializers, sliding doors, annoying alarms – all uniquely recognizable as "Star Trek Sound Effects".
I'll let you in on a secret – Amazon has the Star Trek: Original TV Series Sound Effects CD available as a downloadable MP3 album.
There are 69 tracks on the CD ranging from 6 seconds long to 5:54 including the following tracks:
1. Enterprise Bridge Sequence
2. Enterprise Doors Open Into Corridor
4. Transporter Energize
7. Alien Planet Surface
8. Communicator Beeps
13. Red Alert Klaxon
15. Spock's Viewer On The Bridge
31. Many Tribbles
32. Tribble Coos
46. Disruptor Hits On Hull
57. Warp Drive Malfunctioning
62. Hand Held Medical Scanner
67. Hand Phaser
Since most of these are short, they can be previewed in their entirety(!) straight from Amazon. This seems like a pretty good resource if you're looking for Star Trek sound effects.