Of the 4 majors - Roland Garros (clay) seems to me to have produced the biggest share of "one slam wonders" or, players that only one 1 grand slam title. Some recent names that come to mind are Gaston Gaudio, Albert Costa and Andres Gomez. "Who?", you ask? Exactly.
To answer your question:
Clay: Favors "grinders" and players that are willing to play longer, more drawn out points. Since clay is a slower surface the ball doesn't move through the court as quickly and so players are able to move to get certain shots that wouldn't be as easy to get to on faster surfaces like hard courts. Players that move well and have great footwork also flourish on clay (like Nadal, Djokovic, Murray, etc.). Clay also tends to favor players from nations where clay is the most common court surface found and so the players "grew up" playing on it and were more familiar with how to play on it.
Grass: Favors serve and volley players (though not as much now as it used to) and players with an all-court game (baseline & net). The ball doesn't bounce as high on grass and stays lower so some players are able to handle that better than others. Big serving players are usually rewarded on grass also.
Hard Courts: Hard courts are a fairly neutral surface that don't give one type of player a big advantage over another. Players that can flatten out their shots a little can do well on hard courts but the surface doesn't play a huge role in the outcome of a match between equally skilled opponents. This is why we've seen 4 or 5 hour long matches between the top players at the US Open and the Australian Open.
As far as players that dominated on certain surfaces, but not all, I'd say Pete Sampras is probably the biggest example that comes to mind. He won 14 majors, but not one of those was a victory at the French Open. His best result at the French was making the SemiFinals. This is said to be because clay slows down the points and Sampras' game was based around quick points (serve & volley). Sampras was capable of great clay court tennis from time to time but he was never able to string together 7 great matches in a row at the French Open.