I use about 2 dozen mods but there are a handful I couldn't play without.
ArkInventory - all in one bag mod that lets you sort, separate, and other keep everything in order. This is a must for me as a Druid with at least 4 armor sets on me at anytime.
Bartender - the default UI is very inefficient with space and there isn't much you can do about that unless you can move the default actionbars around on the screen.
Auctioneer - the secret to my success. I will literally make 500g or so per day simply by buying low and selling high (well, and disenchanting). This allows me to bypass the gathering professions all together and get to crafting professions.
Quartz - this is a cast bar mod that doesn't really do any one thing that is irreplaceable but it does a lot of little things that as a whole I could not play without; cast bar (for me, target, focus), tradeskill bars, swing timer, countdowns, in-line latency meter.
Pitbull - again, the default UI falls on its face when it comes to unit frames. Pitbull incorporates a number of mods that I would have to find elsewhere into one addon; druid mana bar, party and raid interfaces suitable for healing, detailed information about player and target, lifebloom bar, and most of all moveable unit frames. I find it hard to play having to crane up to the upper left corner to see if I am about to die or not. Probably a result of having a 24" iMac or just laziness.
I really like the others but I can get by without them:
beql
Chincilla
Clique
CooldownCount
CowTip
DrDamage
ElkBuffBars
EQCompare
Fubar et al
MobInfo2
Omen
oRA2
Prat
Recount
sct et al
xloot