My biggest hate is when games don't let you reset/restart a new game quickly preferably without loading.
It's not so bad if there's a continue option, but especially for really hard games, I'll often know right away when I've messed up and need to restart if I'm going to have any chance at getting further... So I can either waste time losing life after life, wait for some loading and have to pass by the high score screen, wait for some more loading for the game to start again, or I could've been allowed to press a button to start a new game instantly...
In a similar vein: Cut scenes, intros or any other non-essential game screen that you can't skip or bypass... They're cute the first time around, and maybe the third, but after a while I just want to get to the action.