I'd like to name a few and link to wikis so you may also learn more about them.
Odo (Star Trek: Deep Space Nine) Only one of his kind on the station, not very social and doesn't really fit in.
Piccolo (Dragonball Z) VERY antisocial, has acute hearing and stands apart from crowds.
Kosh (Babylon 5) Mysterious and often misunderstood to the point of people fearing him.
Aximili-Esgarrouth-Isthill (Animorphs) The one alien among the group of humans, and he doesn't always behave properly in his human morph.
Sesshoumaru (Inuyasha) Says little when it isn't necessary and sometimes it's hard to guess his motives.
What about you? Which oddball characters do you gravitate to?