I'm a fan of Harry Potter and have read a lot of great stories on this site.
My favorite stories are the ones that keep the characters as close to cannon as possible. No offense intended to those that prefer a different take on them, but to me if you're planning to do a story based on characters from another person's work, it works best if you those characters. It's also something that is not easy to do and so for those that pull it off well (and there are many) I have respect for their skills and I hope I manage to do the same.
As for what I like in a fic:
A strong, semi-independent Harry. In the books I find it both interesting and telling that Harry has very little adult guidance. The closest thing he has to a mentor in the books is probably Albus Dumbledore and I think most can agree that his plans and agenda were shady at best. Harry struggles during his time at Hogwarts and throughout the war but remains resilient. He doesn't give up and he grows into a person that has taken the hardships and pain in their life and allowed it make him stronger but also compassionate. His friendship with Luna is probably the biggest testament to that. Therefore I am constantly surprised that people seem to think that Harry is in desperate need of a mentor (especially in the form of Snape, who I happen to think needs more guidance and care than Harry ever did). However, sometimes this independent streak can be taken to far. I find Harry to be smart but some people have Harry hiding all of skills and intelligence away to 'spare Hermione's feelings' or as some mastermind Slytherin plot and I honestly don't see much point in that.
Not a fan of Bashing Characters:
This is obviously personal preference but I like the Weasleys and I like Hermione and I really can't stand when people feel the need to destroy the entire relationship by stating that the Weasleys were pretending to be friends with Harry this whole time because they were getting paid to do so. Each of the Weasley's have their faults but they are good people and to make the entire relationship a lie is just lazy in my opinion.
I also don't think that Dumbledore was evil the whole time or even that he didn't care about Harry. I think he cared about Harry more than he ever expected to. I think that he was being completely sincere at the end of the series when he explains to Harry that he was always the better man. However, Dumbledore is manipulative and he is known to put what he thinks is good for the Wizarding World before anything else- especially Harry.