I've found that fanfiction can annoy me - I have a low tolerance of fics that take the characters out of character, destroying an old favourite perhaps to further the plot in the author's mind. This is of course, perfectly acceptable, but one would not, for example, wish to read a fanfiction where Harry Potter turned evil as it's not in his character. Nor is it in Snape's character, but we'll leave my hatred of JKR to one side for the moment.
If a fanfic is reasonably well-written and the characters are roughly in character, I'll probably read it, enjoy it and review it accordingly. Most of the reviews I write are good - I rarely leave negative feedback. Also, I try to keep the characters I borrow "in character" as much as possible - I try to think of it like borrowing a treasured toy from a good friend, something that needs to be returned in as good if not better condition. I don't always succeed, but I do try. It irritates me when characters or worlds are destroyed by authors in meaningless ways - either by character assassination, death in a non-believable way or actual destruction of the world (The Last Battle by C.S. Lewis scarred me as a child). If you want to kill a character - fine. But give them a believable death that they deserve and don't reduce them to begging at the end if it's not in their character (wanders off to get a coffee muttering about JKR).
The major thing that annoys me is when authors abandon fanfics half-way through. They have taken the time to come up with an idea, I've enjoyed reading the story and then it dies. As this annoys me so much, I've decided to always finish my fanfics, regardless of whether I like them or not.
I struggled to complete "Choices" as I had a few family problems and the story wanted to go in one way and I in another, but the story won out in the end and as soon as I had time I completed it.
I also hate disappointing people - so even if I did hate a fanfic I was writing, I would continue it to the bitter end just in case someone else loved it. That's why reviews are so important - they encourage me to keep writing! ;-)
I hereby promise to always complete my fanfics - if it appears I've given up on one, it's possible my life's up the creek and I'll be back as soon as possible to finish it.
Someone asked me what my favourite fanfiction that I'd written is. Well, "Endgame" was fun to write, but is rapidly being overtaken by "Circus of Life" as that fic is writing itself and I am actually enjoying writing fluff. My least favourite is "Working for FGM" as it is unpolished. My overall favourite is "The Stepmother's Excuse" as I had great fun fleshing out Eve into a real person instead of a stereotype and I didn't feel obliged to give it a happy ending.
So now you know! ;-)