We all know 'em, the tutorials modern games have. Often mandatory and teaching you the most inane things, basically a retread of the manual. I hate those, they tell you which button is where but afterwards you still can't really play the game, especially for more complex multiplayer games like fighters or RTSes.
The current tutorials are almost a waste of time. I'm not saying they should be removed but I'm saying:
Make tutorials REALLY teach the game!
Knowing controls and some basics isn't knowing the game. Knowing how to order a unit around is not knowing what to do with it. Tutorials must be expanded. They should not just teach how to play but how to play well. In a fighting game a tutorial should teach you how to use a character well, what combos are useful, when to use which special, etc. Things you'd usually look up online. Similarily, in an RTS it should teach you about every unit, how it works in a strategy and what it's really good for, how it should be used in play. In a game with roles in a team it should teach you what your role does, how to do it well, who you need to work with and when you need to leave the job to someone else.
Basically I want tutorials to teach advanced tactics and behaviours. I want someone who finished the tutorial to be able to join a multiplayer game and know what he has to do, even if he can't execute all the details perfectly yet. Lately I've been playing World in Conflict, that game's tutorial should have been teaching support players that they're needed on the field as antiair instead of having some arty in the back and bombarding crap.