The most likely candidates are Superman and Batman but there may have been a couple of other timeless heros who were portrayed by numerous actors over the years. The definition of 'superhero' in this context can be expanded to include such worthies as Hercules, Tarzan, etc.
There's also Tarzan -- according to this page, he has been played by Elmo Lincoln, Gordon Griffith (as a child), James Pierce (Edgar Rice Burroughs' son-in-law!), Gene Pollar, Frank Merrill, Herman Brix, Johnny Weissmuller, Buster Crabbe, Glenn Morris, Denny Miller, Lex Barker, Gordon Scott, Jock Mahoney, Mike Henry, Ron Ely, Miles O'Keeffe, Christopher Lambert, Joe Lara, Wolf Larson, Caspar Van Dien and Travis Fimmel. That's twenty-one, just beating Hercules.
The most prolific character seems to be Hercules. At least twenty actors have put on the loincloth to portray the Greek god. Some better than others.
The first and most successful of these was Steve Reeves. Other actors who played Hercules were Gordon Scott, Kirk Morris, Mickey Hargitay, Mark Forest, Alan Steel, Dan Vadis, Brad Harris, Reg Park, Peter Lupus, Michael Lane, Samson Burke, Arnold Schwarzenegger, Lou Ferrigno, Brian Thompson, Richard Sandrak, Dwayne Johnson, Kellan Lutz, Kevin Sorbo and Mark Addy.
Second place goes the Man Of Steel. Thirteen is the number for the Kryptonian;
1939 - Ray Middleton, 1948 - Kirk Alyn, 1951 - George Reeves, 1961 - Johnny Rockwell, 1966 - Bob Holiday, 1978 - Christopher Reeve, 1979 - Tayfun Demir, 1988 - James Hayes Newton, 1989 - Gerard Christopher, 1993 - Dean Cain, 2001 - Tom Welling, 2006 - Brandon Routh, 2013 - Henry Cavill
Seven actors have played Batman: Lewis G Wilson, Robert Lowrey, Adam West, Michael Keaton, Val Kilmer, George Clooney, Christian Bale
Some of the other notable superheroes apparently have apparently only had a single handful of actors' portrayals.
Note: These do not include child actors or Broadway/stage productions. Neither does it include voice actors or TV commercials.