I recently played a pen-and-paper game (via ventrilo) with a coworker and 3 other friends. It wasn't Dungeons and Dragons. In fact, the game is experimental and yet unpublished (Unsure whether it will be or not).
The intent of the game is to role-play as if your character were one of the stars of an anime series. Before playing, you create a character sheet and write a bunch of skills down that you deem your character has. When you're in any kind of encounter, you pick a skill that seems appropriate and roll the dice. On a pass, you narrate how the encounter plays out. In any character-appropriate way you want.
I noticed that the game's focus is Style. The Game-Master (GM) presented a plot, and essentially, we were guaranteed to succeed in the end. But the important part of the game was that opportunity of succeeding your way.
Players all want something different. I won't take the time to explain how diverse our characters were in the Pen-and-paper game I've been talking about, but they were each completely unique.
Thinking about it, the best video games allow players to do things their way. It's easy to criticize World of Warcraft for forcing players into a tank/dps/healer group structure, but at the same time, each individual player gets to choose from various classes. You also get to choose races, the quests you want to accept, the areas you want to explore--even pvp vs. questing vs. raiding.
Some shooters give you many choices of how to defeat your opponents. Different tools/weapons, and even different results for shooting a monster in the arm versus the leg or torso.
The games that will succeed on a grand scale will cater to each player's style. The current trends point to games doing one thing really well. But fortunately, there are many games to choose from. Find one that suits your style or play one that lets everybody play their way. What really matters is doing things your way.