Here's a list of what I'm running right now (best ones are
bolded):
Borderless Cyrodiil (removes the annoying borders at the edge of Cyrodiil)
Clocks of Cyrodiil (adds clocks to almost every bar and tavern, and even adds huge clocktowers to Leyawiin and Chorrol)
Alive Waters + Koi and Slaughterfish addons (adds tons of underwater plantlife, a lot of new fish species, and even adds huge shipwrecks and other underwater treasures)
Midas Magic Spells (adds over 100 totally new and awesome spells that you create yourself from ingredients gathered from plants, animals, and jewelry. Most of these spells are totally amazing and range from crazy conjured creatures to interdimensional travel)
No Psychic Guards (city guards no longer come rushing in from miles away when you attack or steal from somebody)
Real Lava (makes the lava of Oblivion actually look like real lava, and not tomato soup)
Unofficial Oblivion Patch (patches over 1000 bugs ignored by Bethesda)
The Lost Spires (adds a whole new questline, tons of new items, and huge dungeons So far this mod has the most polish out of any quest addons I've seen so far)
Thievery in the Imperial City (adds 11 new quests that involve stealing things from folks in the Imperial City. It also adds throwing potions that paralyze, blind, and set fire to people. After the first few quests a pretty cool storyline will emerge but I thought it was too short and the cliffhanger dissapointing)
Ruined Tail's Tale (adds an Argonian companion that will fight for you. He also comes with a storyline that you can either ignore or get involved in. Your decisions play a big part in what happens if you decide to get involved. You can also share equipment with him.
Oddbasket Glass Replacements (if you think the default neon-green glass textures for weapons and armor are an eyesore, this is what you want. It makes all the glass weapons and armor actually look like they're made of glass)
Longer Days Shorter Nights (time passes slower in the daytime, while it goes quicker at night)
Better Water (makes water clearer and less muddy)
BT Mod (shrinks the menu text so you can see more items at once)
I highly reccomend that you download ALL of these mods. I've researched, played, and tested them all myself and I assure you there's no problems with any of them and that every single one is more than worth the download. I hope this list helps.
None of these mods drastically change the game itself, but if you want a whole new experience (or if you're disgusted with vanilla Oblivion) you should get
Oscuro's Oblivion Overhaul. I have not tried this mod myself, but it seems to be pretty popular, and I'm also not sure if this mod is compatible with the ones listed above.