I thought self-inserts were a bad thing ._.'
Shows what I know XP
I've already mentioned one time-travel fic in kakteed's thread, but here's another one I just found out about the other day: The Moment It Began. I haven't read it myself yet, so I don't know if it's good or bad, but the premise is that Snape gets a second chance at living his life and changing it where it all went pear-shaped.
Run That By Me Again is sort of self-insert in that Harry and Hermione now reason the same way the writer would have. There's not really any plot, just scenes from the books rewritten with a hefty dose of "why didn't they do it like this". Some chapters are better than others, a few are hilarious.
Now, I've spent about two hours going through my favourite fanfics, and I've come to the conclusion that I don't read a lot of crossovers or Peggy-Sue fics. I couldn't tempt you with some Harry crack!fic perhaps?