And here's a couple that I remember seeing variations on back in the day but haven't seen them done in a while:
* Snape is a vampire and needs a willing donor/host to provide nutrients otherwise he'll die/loose control of his faculties and become a danger to others. Remus volunteers/is contracted into an arrangement with Snape because he is already a werewolf and therefore cannot be turned into a vampire, plus his blood is extra rich with magic and whatnot because of his lycanthropy.
* Remus was bonded/mated to Sirius (yeah, I know "Blech puppies!") and after Sirius falls through the veil, Remus must find someone else to bond/mate with or else he'll die too.
* Tonks is obsessed with Remus because she's under Imperio/a love potion. Snape recognizes the symptoms/discovers the plot through his spying and cures her. Remus is very grateful. ;)