I don't use a ton of mods -- after a bit of a problem occured and I had to uninstall and re-install my Oblivion game, losing all of my mods in the process -- but there are a few that are priceless.
My favorite mods - most of them include companions, but whatever.
Ruined-Tail's Tale An Argonian Battlemage. A wonderful companion mod. Ruin has a shady past and thinks on his own terms. Great scripted effects in here.
Companion Share Recruit If I could choose only one mod, it would be this one. It lets you turn anybody in the world (Who has the rumors option available) into a companion!
Tears of the Fiend HUGE Companion/Quest mod. To start the mod, simply sleep. This mod gives an absolutely breathtaking questline. At the end of the quest, you can get two companions... if you are lucky. A slight warning, I relied heavily on the guide it came with - it can be complicated at times.
Despite what some think, you do need some company after a hard day being a hero (and maybe during the day, too).
Companion Vilja A Nord Alchemist. A fully voiced companion, Vilja is on a mission (Won't tell you what) and wants a bodyguard when she does it. Vilja has such an advanced AI, you'd think it's just I. :)
Cm Partners Mod Basic This mod adds over 70 npcs in local Taverns, Inns, and Guilds. They all are available companions, and have advanced orders such as "Sleep, Practice Archery, Eat, and Loot". Perhaps the best thing about this mod is the how easily you can create your own partners. It comes with a very simple guide.
Alluring Potion Bottles Version Three You won't truly appreciate potions and poisons until you see these. It's almost a shame to use up them now.
Natural Environemnts This makes Cyrodiil a much better, place, making weather better, trees bigger, and adds birds and insects to Cyrodiil.
Other Handy Mods
Set Essential Actors Plus Have you ever wanted to make a Companion essential? Guess what? This mod does it... and more! You can flip on and off the Essential Status, Respawn Status, No Rumors Status, No Persuasion Status, and Quest Item status.
Master of Puppets This spell lets you Take Control of any NPC! (Well, not really, you turn invisible and walk behind them, and every thing you do, they do.) I found it quite fun to take control of First Mate Malvulis and drown her. You cannot attack with controlled people.
Just for Fun
Hilarity This mods adds several spells to Edgar's in the Market District. Included: Failed Levitate, Summon Bandit Gang, Transform into Sheep, and Summon Titan Ogre.
28 Days and a bit - ZOMBIES! (Warning! Before you even activate the mod, create a save game you can load to before you start the events this mod provides) -- Perhaps the most fun "I'm bored" mod - this mod simulates a zombie outbreak in Cyrodiil. Read the description for more fun...
Midas Magic About 300 new spells to the game. Enough said. Turn bodies to gold, go to the astral realm, and my favorite: Astral Combat. It is a spell that teleports you and one enemy to a small arena for one on one combat.
Supreme Magicka Adds new spells and balances existing ones. Makes mages stronger.