No he doesn't. RON marries Hermione. And HARRY marries Ginny. Harry+Hermione... Yuck. Don't believe me? Books six and especially seven are proof. Whoever asked this question is either VERY stupid, or never even read any of the Harry Potter books, because the vast majority of us knew who was gonna end up with who by the end of the second book. Read the books. She has always only been like a sister to him.
Ok now thats just rude. It can easily be thought he did earlier in the series and it is clear at some time there was an emotional connection between them, J.K Rowling even said that during the tent scene in the last book things got heated and while alone they depended on eachother they have been close since book 1 so romantic feelings wouldnt be surprising. Harry does however think of her as a sister and so there were no romantic feelings at this point.