I liked Evil Genius because it offered you a tutorial for the real basics, and also provided help during normal games, further explaining gameplay Mechanics.
Also Prince of Persia has a good feel to it since you don't actually have to play a tutorial, everything just gets explained while playing.
Psychonauts of course has an easy ride because, as Yahtzee said, the entire first half of the game is nothing more than a tutorial.

I liked Call of Duty 1's. It was basically how I had seen it in my mind for a war game.

Of course, Crysis has a fun first level.

Hmm, and uhh, Half-Life 2. It builds its tutorials inside the game.

Morrowwind was good, brief, to the point and straight into the game, I just wish that some of the more complicated mechanics were explained, like enchantments.

My favourite is probably Chronicles of Riddick: Escape from Butcher's Bay, First your told how to look around and the move keys, then straight after that window fades: "Approach Johns from behind, Right Click to kill Johns. Avoid auto turrents."

Other than that probably Destroy All Humans...

I can always appreciate when games fit bit-by-bit tutorials into their opening story levels without dumbing it down too much, creating a level solely for a tutorial, or blocking the use of basic moves until it tells you how to use them. This is what happens in:

-God of War
-Metroid Prime (1-3)
-Turok: Dinosaur Hunter

Also of honorable mention is Star Fox 64's tutorial- it used an intro level unrelated to the story to introduce Missile Locks, Loops, Half Loops and other fancy things, but it had it's own little secret; if you killed 100 enemies a Star Wolf craft would show up.

Grampy_bone:
I liked Thief and System Shock 2's tutorial levels.
System Shock 2 was the army recruiting programs!

I agree with both Half-Life's and CoD. System Shock 2 had a great tutorial, but the little in-game blurbs that you had to read were really annoying, because you could easily miss one and not know what to do, and stopping to read them killed the immersion of the early levels.

The LotR movie games had excellent tutorials; when I play RotK with friends, I let them go through the tutorial and they usually are competent enough to play through the rest of the game with me in co-op and generally know what they're doing.

Elurindel:
Jack, from Vampire the Masquerade: Bloodlines. He was the greatest tutorial ever. Cool and kickass, and didn't give a crap about anybody, but willing to spend just enough time to stop you from swallowing your own fists.

"We're living in the age of the internet and cellphone cameras. F@#! ups ain't tolerated."

Jack is the win. Epic, pure win.

Another good tutorial would be the tutorial from Myth II. <throws explosive, blows a dummy to pieces> KABOOM! He's not getting up again.

The tutorials in Psychoauts are fun, and they better be since they go on for so damn long.

I didn't mind the tutorial from KH1/2. That, and COD4's.

Kingdom hearts games do it great, there are some others games i remember playing over and over the tutorial but cannot remember which ones.

I cannot belive no one has said GTA especially 4. You are just given beginer missions and the skills needed are shown in a little tooltip.

TF2 Tutorial.Pick a public server, get thrown into the whole clusterfucking chaos and fight your way into 1337-ness.

Oblivion's was excellent. Grabs you by the balls like the start of an excellent film, takes you through a nice and easy dungeon so you get the start of a feel for the mechanics then when you exit the sewers you're cast into a beautifully endless and endlessly beautiful world in which you can do as you please. But you'll probably die.

I really liked CoD4's tutorial-ish level, that is to say, the ship mock-up.
Mostly the competitive element; setting times through the course, then being told how well you scored and recommended a difficulty.

SurferRosa:
Oblivion's was excellent. Grabs you by the balls like the start of an excellent film, takes you through a nice and easy dungeon so you get the start of a feel for the mechanics then when you exit the sewers you're cast into a beautifully endless and endlessly beautiful world in which you can do as you please. But you'll probably die.

For my main problem with the Oblivion tutorial, read my Oblivion review. Specifically, the plot summary.

The Carrington Institute.