Well they aren't always three letters! I originally posted this in response to someone's query, but thought a stickied post would be useful! Feel free to add more!
General
LFG - Looking for Group
LF(#)M - Looking for # More
PVE - Player vs Environment
PvP - Player vs Player or sPvP - structured Player vs Player (these are basically the same thing)
PvX - Player vs All
WvW - World vs World
TS - Teamspeak
AoE - Area of Effect
DPS - Damage per Second
XP - Experience
TP - Trading Post
WP - Waypoint
PoI - Point of Interest
JP - Jumping Puzzle
SP - Skill Point
OSD - OverShardDistrict (a particular instance of a Megaserver map, still trying to get this one to catch on!)
CC - Crowd Control (refers to conditions which like cripple, immobilised, stun, chilled, which impede the movement of the enemy)
Dungeons
CoF - Citadel of Flame
CoE - Crucible of Eternity
HotW - Honor of the Waves
AC - Ascalon Catacombs
TA - Twilight Arbor
SE - Sorrow's Embrace
CM - Cadecus Manor
FotM - Fractal of the Mists
(P1,P2,P3,P4 refers to a path of a dungeon usually used in conjunction with the above, eg. LF2M HOTW P1)
Other
BoH - Badges of Honor (reward from WvW)
AR - Agony Resist (only relevant to Fractals)
DS - Death Shroud (Necromancer profession skill)
PVT - Power Vitality Toughness (popular defensive item stat combo)
Servers
NSP - Northern Shiverpeaks (The only one you need to know!)
BG - Blackgate
IoJ - Isle of Janthir
JQ - Jade Quarry