I'll post this one because most people will have never heard of it:
Rob Machado's high-five with Kelly Slater at the 1995 Pipe Masters.
Since no-one has ever heard of it, here's the explanation:
The Pipe Masters is a surfing competition. It's held at Pipeline on Oahu's North Shore in Hawaii every winter, and is the last contest of the year for surfing's World Championship Tour (and, as of 2005, has $270,000 in prize money). In 1995 the final heat at the Pipe Masters was between defending world champion Kelly Slater, and Rob Machado, who was ranked second in the standings. This final heat would determine the world champion for 1995 (not to mention who walks home with the prize money). The waves that day were good, and both competitors were putting in great performances. Slater had caught a wave, and was paddling back out when Machado caught another wave behind him. Machado's wave was a great wave, and when he came of the tube at the end, Slater was right there paddling out past him. What happened? Slater held up his hand and Machado, with a big smile on his face, slapped him five as he surfed by.
It was a display of sportsmanship and of love for the sport, rather than the money or the spotlight, that you just don't see that often in professional sports.
BTW, Slater went on to win the heat, and the championship, and the next three championships after that, until he retired after the 1998 season.
I thought I'd post that since everyone else will have baseball/basketball/football/etc stories.