Aw, Harry/Luna are cute. Whilst I have always been/will always be a true H/G and R/Hr Shipper, I have enjoyed pairing Luna with just about everyone at some point or other in fandom. She is such a unique, fresh character with such an interesting dynamic with so many people - I find I can enjoy Harry/Luna, Ron/Luna, even Draco/Luna in fanart and fanfiction. In the books however, the nearest I've got to shipping Luna with someone is Dean for a while during the seventh book and more generally, Neville.
But yeah, good idea for a thread! For me the things which I like about Harry and Luna together are that she is so positive and free in herself, a breath of fresh air for Harry, and open-minded enough that she is one of few who are really capable of understanding him. The loss of their mother is also a bond they both share. Harry likewise, as an outsider himself, is more capable than most of understanding - and even being attracted to - Luna's loneliness and unconventional ways. They are both people who will never quite fit into 'normal' society, so I think there's a lot of common ground there which could have been a good basis had Harry and Luna been put together romantically.