Obviously you'll want to have
Oblivion Mod Manager
Oblivion Script Extender
and maybe WryeBash (it's a bit more technical but a must if you want a weather mod)
Body Mods
Robert's Male body version 5
Exnem's eyecandy body replacer (seems to be the best supported female body mod though it's a bit cartoony. Choose robert's female body for something more realistic).
Random Mods I enjoy.
Quarl's Texture pack 3 redimized (does wonders for oblivion's textures)
Millstone Farm - awesome house mod! Just downloaded it and it's incredibly detailed. Korana is the best.
Unique Landscapes - these are a must. Makes oblivion's wilderness feel like just that.
Animated Window Lighting System - does what it says ... and it does it well
All Natural - best weather mod out there.
Immersive Interiors - You can see out of windows! Still a WIP
Symphony of Violence - nice sound replacer for combat
Alive Waters - adds some much needed detail to underwater Oblivion.
RealSwords - adds race specific weapons to npcs (Khajiit, Argonian, Breton, Bosmer, Nord, Redguard)
Slofs Horses - Texture replacer for horses. It's pretty amazing.
Mad Mages Tower - awesome home for a mage with some great touches (moving walls, a crazy chest)
New Face Textures by enyala - my favorite face texture mod
Slofs Khajiit Retexture
Morrowind Themed Mods I enjoy.
McMuffin's Daedric Lord Armor - Incredible recreation of morrowind's daedric armor.
Dwemer Skyship by mr_siika - awesome floating house mod. The miscellaneous dwemer meshes are spot on.
Personal Pack Guars - Adds guars to Oblivion ... huzzah.
Morrowind Booze
Morrowind Books
Some of My Mods
If you start aching for Morrowind Equipment try Vvardenfell Imports and Vvardenfell Imports Addon. Adds a shop to cheydinhal just be sure to check the bookcase
Mythic Animals
Mythic Creatures
Mythic Ghouls and Ghosts - High res texture replacers for Oblivion creatures.