I use www.freegolftracker.com
I've been using it for 4 years now, and am pretty satisfied with it. It will keep your handicap and also stats like
Fairways hit, Greens in Regulation, Putts, Chipping Stats, even Greens Fee costs, if you care to enter all of that
info. It's the first thing I do after I get home from a round....takes about 5 minutes, and yields a wealth of information.