I've got quite a few, and since I've done just about every class and role at some point, I've seen a lot.
On my Merc (ordinarily DPS, but I know how to heal too), I was grouped as a healer and one of the DPS asked me not to heal her because she didn't like all the green stuff getting on her clothes
A Scrapper Scoundrel who charged into combat with no armor on, not stealthed, after typing various silly battlecries (Directive 7 NM, IIRC). Died in every single pull. (Technically, this was a pre-GF PUG)
An Assassin tank who wouldn't guard my Op healer, a Twi'lek, because she was a "filthy alien". I didn't ask for one, he just felt the need to announce it.
On my first HM on my Jugg tank, there was a fairly well-geared smash marauder in the group who would randomly AFK for 5-10 min at a time, then inexplicably leap into the middle of a pull and kill everything, wash, rinse, and repeat, all without saying a word.
This is a catch-all, but there are a number of people who seem to want to ERP with my Sorc healer, and want to spend the better part of the FP propositioning me in whispers.