Little Black Dress

Some fans do not Ship a particular pairing, but instead prefer to read/write about a single character. These fans will read anything including their favorite, no matter whom he/she is paired with.

This character is often referred to as a little black dress or LBD because he/she goes with everything (literally in some cases).

The PPC has its own LBD character in the form of Agent Luxury.

Notable LBDs
Buffy the Vampire Slayer has Spike, who, even in canon, has been paired with several regular characters.

Transformers has the character Starscream (who has appeared in some VERY weird pairings).

Harry Potter has...well nearly every main character appears to be a LBD in fanon. Professor Snape and Sirius Black seem to get the LBD treatment a lot.

And who can forget Captain Jack Harkness from Doctor Who?

Tails from the Sonic universe is also a good candidate. Even though he's eight years old.