The divide between mediocre players and master level players increases as time goes on. No longer is there the full spectrum of players be paired against. Instead, most of the player population has gotten good at the game and they are the only competition left.
If you're looking for some specific examples, think along the lines of the Halo or StarCraft series.
Where there is a lot of competition to be found.
As the total population playing the game decreases, the average skill level of each player rises. The longer the game has been around, the higher the average skill level will be. Not everyone will be a master of the game, but everyone will continue to get better.
The ramification of this is a huge barrier that a new player must conquer to enjoy the competitive portion of the game. It's no fun getting annihilated every single round but that's the prospect a noob faces when entering a long established game. We all want to match minds with opponents of equal skill level, but when the general population of a game is really good it becomes much more difficult to find even matches on the low end of the scale.
There needs to be a way to teach new players about the game without them getting destroyed repetitively. A mentor system with rewards for both players can go far. Tutorials on advanced concepts are also a welcome addition. No matter how it's done, there needs to be a way to bridge the gap between masters and the mediocre, otherwise the population of the game with dwindle until it disappears completely.