For me the funniest moment was when me and an IRL friend was sitting on skype discussing the game, only to realize we were both on the same planet(we play different factions on the server we played on though, for Epic Personal Duel(EPD) reasons). We decided to have an EPD at the Sarlacc pit on Tatooine. So we got there, started fighting, and the first thing that happens is that he force pushes me into the Sarlacc pit. Being a Bounty Hunter I found it hilarious.
Also, the Sith Warrior scene on Dromund Kaas when the two groups of bounty hunters come for the carbonized republic prisoner. I had my Sith Warrior threaten both groups by shouting "I AM GOING TO TEAR YOUR FLESH OFF AND EAT IT RAW!!!".
This scared on of the Bounty Hunter leader, but the other assured him that I was not serious before nervously asking me if I really was going to eat them.
My Sith took an awkward staring pause before sighing out and calmly say "It was just a figure of speech really." and both hunters immediatley went "OHH! Well in that case!" *lifts guns*
My Sith Warrior's solution was similarly funny: he goaded the groups into killing each other while the Imperials move the prisoner.