Dominos Classic - Minimalist action bars
Questie - A quest helper (little buggy but helpful)
ClassicAuraDurations - Restores cooldown swipe timers
OneBag3 - One bag to rule them all!
ClassicCastbars - Adds castbars to TargetFrame and nameplates
Auctionator - Improved auction management
Real Mob Health - Displays health numbers for mobs
DBM-Classic - Deadly Boss Mods - Don't stand in the fire!
Vendor Price - Tries to replicate displaying the vendor price of items
Coordinates by TomCat’s Tours - Map coordinates

These are the mods that I'm currently running.  Listed in order of how much they have enhanced my game experience to this point.  In vanilla, I never used a UI mod (at least not one that I stuck with for more than a night).  I love Dominos.  It's super easy and very clean.  There's a screen on our discord chat page.

Feel free to add your favs to this thread.

Bagnon has now been updated and works in Classic. That is my preferred bag add on.