So since most of the Star Trek pilots have had something to do with the plot,
- TOS - Where No Man Has Gone Before (deals with the barrier at the edge of the Milky way galaxy)
- TNG - Encounter at Farpoint (deals with those weird Alien jellyfish thingys and the encounter with Q)
- DS9 - Emissary (deals with sisko finding out that he's the Emissary of the Prophets)
- Voyager - Caretaker (deals with the caretaker entity stranding the voyager in the delta quadrant)
- Enterprise - Broken Bow - deals with Earth's first contact with the Klingons in Broken Bow, Oklahoma.