Simple and common :
LOL - laugh out loud (spawns from orignal : Lollercoaster, lollercaust)
ROFL - rolling on the floor laughing (spawns from original : Roffle, rofflecopter)
LMAO - laughing my ass off
WTF - what the fuck?
OMG - oh my God
IMO - in my opinion (IMHO - in my humble opinion)
BTW - by the way
PITA - pain in the ass
BRB - be right back
FYI - for your information
AFAIK - as far as I know
TIA - thanks in advanced
AFK - away from keyboard (users is not there)
BBL - be back later
IIRC - if I remember correctly
RTFM - read the fucking manual
Not as common :
FTW - for the win (aka : the best choice, a very good choice.)
ex. What kinda pants should I get for work? - Dickies pants FTW.
x4L - (x being a variable) for life
ex. Verizon4L (Verizon for life, I won’t switch to any other cell phone provider)
Nerd Speak :
RPG - role playing game
MMO - massively multiplayer online
I can’t think of anything else. Feel free to add stuff.