Is a player in checkers required to take a jump if one is available? What about a double or triple jump if that is available?
In short -- for tournaments, yes.
I never played with forced jumps as a kid, but my father-in-law always plays with forced jumps. So I did a little digging around, and this is what I found:
The American Checker Federation seems to be the only sanctioned checkers organization I could find. According to the American Checker Federation, rule #1.20 says
1.20 All capturing moves are compulsory, whether offered actively or passively...
There are many variants of checkers/draughts, and for all of them (including the Checkers variant played predominantly in the English-speaking world), not only is jumping compulsory, it is also compulsory to keep jumping until all the jumps are completed. Quote from the American Checkers Federation's official rulebook:
1.19 If a jump creates an immediate further capturing opportunity, then the capturing move of the piece (man or king) is continued until all the jumps are completed. The only exception is that if a man reaches the king-row by means of a capturing move it then becomes a king but may not make any further jumps until their opponent has moved. At the end of the capturing sequence, all captured pieces are removed from the board.
1.20 All capturing moves are compulsory, whether offered actively or passively. If there are two or more ways to jump, a player may select any one that they wish, not necessarily that which gains the most pieces. Once started, a multiple jump must be carried through to completion. A man can only be jumped once during a multiple jumping sequence.
However, the rules for selecting among multiple ways to jump differs from variant to variant. E.g. for International draughts, the sequence with the most jumped pieces has to be selected, and for Italian draughts there are even further tie-breaker rules depending on the number of kings that are being captured.
There are many different Checkers variants, but I believe most of them use a forced capture rule.
I've always had the same rules that this article does (Rule 9), if you can jump, you have to jump at least once, but you don't have to jump any more than that.