I've come across variations on draughts, as I've always called it - we had a compendium of games that came in a cube - it had six sides on it, one of which was a checkered board for playing chess and draughts on.

With draughts, apart from the traditional version, there were the following variations:

Dammspiel - that's what the manual called it - I think it's also called Damenspiel - you set them up a bit like chess, but they were placed one square forward (hard to explain) - the pieces moved almost identical to regular draughts - diagonally, one square - I think the kings could move multiple squares - a bit like the "Flying Kings" rule people have mentioned - except that you stop short of capturing - my memory is hazy on the issue.

Turkish Checkers - similar set-tup to Dammspiel/Damenspiel - it looks a bit like chess with draughts pieces, the set-up being on the same squares you'd use for draughts - pieces move one square forwards, and, if I remember rigtly, capture diagonally, like standard draughts - the kings, I believe, move like rooks in chess and jump only once in a straight line - again, my memory is hazy regarding the rules.

One game not listed in the manual was a game known by one of three names - Arrow Draughts, Dagger Draughts or Kings.

Played similar to standard draughts - you play it corner-to-corner and set the pieces up as kings in the shape of an arrow or dagger - you then play it like regular draughts.

I have played draughts with at least three opponents - a relative, somebody at school and somebody I once shared a house with - and they were convinced that a single man can't take a king.  Apparently, according to this page, that's the rules in Italian draughts.