I have some:
Luna and Neville- because well, this is adorable. Luna is so unique and I think people don't really give her a chance. Yes, she's odd. That's just her thing. It makes her quirky and not the typical girl. As for Neville, since the start he has always been that clumsy kid you feel sorry for. But he's also a good listener, he's patient and he's loyal.
Hermione and Tom Riddle Jr OR Hermione and Draco- Whenever I say I ship Hermione and Riddle there is always that one person that howls at me in frustration. But here's why. I absolutely loathe Ron and Hermione. I feel like she needs someone to challenge her and intellectually stimulate her. Who better then the future Dark Lord? He's smart, he's handsome, he's bloody brilliant at magic, and it makes for some amazing time travel fanfiction. I've got the bookmarks to prove it. xD
As for Hermione and Draco, it's like fire and water. It's like how I ship Katara from ATLA with Zuko. They hate each other, they fight all the time, but darn it all! They would make a bloody fantastic couple. The same applies here. Sure they would fight, and their both rather stubborn and would refuse to give in, but I think once Hermione is able to get him to accept the fact that there is nothing wrong with her being a 'mudblood', then I think they would be cute.
Severus and Lily- This i'm not even going to explain. If you've read the books or seen the movies then you'll just know.
Thanks for your time everyone. ^-^