Already answered this in another thread with a few more questions... but since this thread is dedicated to this one question only, here's a more "detailed" answer. Not sorted by any ranking, because there's no ranking at all.
First there's Severus Snape. The only one of my three favourites being in the books right from the first one. And reading the books for the first time about thirteen years ago my only thought was "I like this guy!"
Of course his later actions and all the things that were revealed later are what made him "popular" among the fans. For me, those revelations (honestly) are just an addition, amplifying the "There's someone I can identify with" feeling. And regarding his childhood he's not a hero at all. He's mainly a socially awkward guy looking unkempt and (sorry, fangirls!) ugly.
Next one is Remus Lupin. For him it also started with plain "sympathy". And maybe the fact that he was different from other people in some way. One of my closest friends is very similar to Remus, so this might also add some personal emphasis. (Not to mention the love for chocolate)
Last but not least, Luna Lovegood. Like the two characters mentioned before, she's also different and quite weird, but the only one who doesn't care what others think at all when she behaves some way (as long as it doesn't hurt them). No matter how bad things are, Luna always carried some kind of light and optimism. And that's something that clearly makes her the "hero" for those who are outsiders. Even weird people can be the happy ones.
Sorry for this extremely long post and the typos you'll probably find.
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