1. A small greasy fellow with flaky skin who watches so much Star Trek that he can fluently speak Klingon. Showers infrequently. Dresses up as Captain Kirk and tries to get autographs from washed up 70's sci-fi actors, who have no other means with which to pay their bills but to show up at conventions.
2. Less strictly speaking, a trekky can basically be anyone who has an unhealthy obsession with something that no one else cares about - probably because it's incredibly boring e.g. online gaming.
Trekky: Kliuft d'hif ackked trebluiq gholss'd... *bzarg!*
Person who bathed last night: Look! It's William Shatner!
Person who bathed last night: *runs away real quick*
A fan of the TV show series "Star Trek".
Matt: Do you like Star Trek?
Mike: Yeah man, I am a hardcore Trekky.