Here are my suggestions for Skyrim's tutorial:
1. Keep it very simple and basic. Morrowind's tutorial was perfect in this regard. Create your character. Walk around, pick up a few items, get introduced to the interface, menus, etc. Maybe pick a lock or two. Then, you're on your own...
2. No major interuptions with tutorial tips, or at least make sure they are well-timed. For example, try not to interupt any major battles with an untimely tip: "Your health is running low".... etc.
3. No major battles during the tutorial. How am I supposed to defeat two rats when I haven't yet even learned how to cast a spell or ready a weapon?
4. Make sure that, right from the start, the character can develop in any direction. In Oblivion's tutorial, the only useful spells available were in destrucion and restoration schools. To my knowledge, for example, no conjuration spells were available until right before you go down into the sewers. Any/every skill should be available to use and develop to an equal degree.
5. I'm not even sure how to suggest this suggestion: At the time, I couldn't understand how/why I went up 10 skill levels in Destruction during part of the tutorial, but then somehow "lost" them and instead only went up 2.... Same thing with Sneak--I gained a bunch of levels in sneak, but after talking to the King at a later time, it turned out I only gained one. Although I understand now why this occured, it was very frustrating at the time because there was no explanation for it. So, I guess my suggestion is to either not have this type of thing occur in Skyrim's tutorial, or at the very least explain it thoroughly so it's understood why it's happening.
I am hoping to see more suggestions from others with the hope that our suggestions can be implemented into Skyrim before it's too late.... :]