Split singles. I file them with Compilations, but it seems so wrong.

I don't have a separate section for compilations. I file those by title.

Split singles. I have a few. Generally, I file them based on who I like more or own more of.

For instance, the Iron & Wine & Calexico would be under I because I own everything by Iron & Wine and nothing by Calexico.

If it's two bands that you love equally, I don't know. Tough call, but I'd probably choose whoever was listed first on the spine.

Various Artists?

EDIT: I'm thinking of how I'd tag/file the MP3s, not file the physical CD, so nevermind.

All rules are arbitary, so just pick one that's easy to remember - the band whose name comes first. So if it's a Polediver/Vestibule split, file it under P.

Actually, that's not a split, that's a collaboration. It's the same problem, so I'm only being pedantic.

my filing system consists of precariously balanced stacks and piles all over the floor, in cupboards, on bookcases etc

I file under the A-side if there's a distinct A-side/B-side. Else at the end with comps/samplers.

If you're really torn, buy two copies and file one under each artist.

Or, if you're cheap (like me), get a card and put it in the other place (a "pointer", as it were).