I'm not a big fan of non-canon pairings in most series *if they interfere with a canon pairing*
For example, Usually I'm not big on Draco/Ginny or Harry/Hermione in Harry Potter, etc. (If it's a story where they DON'T end up together in the end, I'd be more willing to read that.)
However, if you wanted to ship, say, Dean Thomas and Parvati Patil from HP or Lassiter and an OC from Psych, I don't mind those because they don't interfere with any canon relationships. I hope that made some sort of sense.
*As an aside, I won't do ANY Snape/Lily pairings. As far as I'm concerned, they were best friends, but nothing more. Snape wanting Lily with her not returning the feelings is fine.
I'm extremely critical of OC's. Let's be honest, 99% of them are Mary Sues, even if done unintentionally. That doesn't mean I won't do stories with an OC, but if one of the main characters is an OC, I will do everything in my power to help you keep them from becoming a Mary Sue.
If you have a non-canon pairing or an OC, prove to me in your request WHY I should choose your story. Otherwise chances are I won't consider the story. Explain to me how your OC or pairing is different than all the bad ones out there.
Of course in song parodies, anything goes! All my preferences fly out the window!