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I have a idea what it is but I wanted to hear other opinions.

Wow, there are so many! And it's going to depend on your character class and preferred style of playing.

I think the best way I personally could answer this would be to list the various skills in the order that I like to use them, with a brief comment about each one. This will take a bit of time and thought.

Sneak

I read a video comment on YouTube and agree with it. The BEST, most overpowered, jack of all trades skill on Oblivion is ... Restoration ...
You can't play if your dead.
Being a magic skill; you'll need a character with a large magic pool. Breton or Altmer. Possibly one of the other races with a star sign of Mage or Apprentice. Breton, with their willpower of 50 would be able to spam up to 100 Restoration before level 2 and still have enough to max out willpower with Destruction or Alteration. You can cast the starting heal self spell whether your injured or not to level the skill. For some of these spells you'll need access to a spell making altar. Healing is obvious. Need a offensive spell ? Absorb health can be deadly to enemies. Fighting a spell caster ? Resist magic could really help. Running low on magic ? Absorb some or fortify your magic before you engage.
Now if you have the Jone stone when you get 10 renown, spell making in restoration really opens up and makes your character a jack of all trades. Doing battle with marauders ? Cast fortify blade. Fortify block and fortify armor work too. Want to get good prices ? Fortify Mercantile. Trouble picking that lock ? make it easy. Need to sneak for the thieves guild ? Fortify that sneak skill.
Point being, you don't have to be great all the time. Just be great at one thing for a few seconds.

I was expecting that I would have to disagree with you, because I figured it would come down to "What is your favorite skill in Oblivion?" But I have to agree that Restoration is definitely one of the most important skills, if not the most important one. You can craft healing potions with Alchemy, but you have to have the necessary ingredients. Or you can buy or find/loot healing potions. But Magicka regenerates automatically, and Heal Minor Wounds is one of the spells you start with (and is arguably the only Restoration spell you really need), plus Restoration is a very desirable skill regardless of your character class. So I think I agree with you 100%.

Funny, I never use Restoration. Building it bores the snot out of me. I'll vote for Alchemy at maximum difficulty and Sneak at normal difficulty.

I use Restoration constantly.

I use Alchemy a great deal, too-- but I almost always sell the potions and poisons that I craft, with the rare exception of a Cure Disease or a Restore attribute potion in cases where I don't have ready access to a shrine or a temple and I don't have the necessary spell or a high enough skill level to take care of something myself.

It's certainly not Sneak. I'm about to start the "Boots of Springheel Jak" quest with a Sneak skill of 10

Alchemy , it is good at higher levels but your limited to when the better equipment is available. Hey Chicken Slayer, do you think someone could role play a character who does not use magic at all ? Using alchemy, base enchanted items but not crafted enchanted items.

"Hey Chicken Slayer, do you think someone could role play a character who does not use magic at all ?"

My usual/favorite way of playing the game is with iron and steel arrows, two copies of level 19 Hatreds Soul (one enchanted, one charged) and the Ring of Kajiit. I can recharge the bow with Varla stones and charged soul gems I find. If you go through all 60(?) oblivion gates you can get around eleven bows.--Plus you can use the Hatred's mace as well to stun enemies so you can finish them off with mundane sneak bonus arrows. It helps to either carry a Silence bow (common in random loot) or use silence poison to deal with spider deadra and Xivilai.
You can play a similar game using the Ebony sword, Gold Brand, and the Hatred's Mace, but you have to do a lot more recharging of souls. Using Umbra for soul traping would probably save you from having to use a soul trapping spell.
Can you comfortably play a full medium difficulty game to level 50 without any magical items or alchemy? Probably not comfortably (i.e. it would drive you insane like trying to play a max difficulty game with no spells, alchemy, or custom weapons)