Must a player take a jump in checkers?
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...