As a power gamer, you want to make your character as effective as possible while playing inside the rules of the game. (If you are happy to bend or break the rules, by the way, you're a munchkin, not a power gamer.) It's not that you want to be the most potent character, necessarily, but that you see the game as a complicated set of interacting systems, and there is a deep satisfaction to be had in finding the most elegant interaction of those systems to accomplish your goals in the game.
And that satisfaction grows when you limit the systems available in meeting your goal. Put more simply, it's a challenge to do more with less. Sure, anyone with access to a full wood shop can make a model boat, but can you make one using only toothpicks and Elmer's Glue? Anyone can write a poem, but can you write 14 lines of iambic pentameter in the Shakespearean mode? Same thing in Dungeons and Dragons -- sure, anyone can create a Tiger-Totem Barbarian Clansman using the full array of splat-books that are out there, but can you do it using just the Core Rules? That would be a goal worth pursuing!
Yes, for most players, the goal of the game is to be the best monster-killer. But a true power gamer gets his rosy happy glow from finding optimal ways to satisfy other goals, too. How do you make the best Explorer-Merchant possible? The best cleric of a God of Thieves? The best Bounty Hunter? None of those characters -- optimized not for solving the problem of combat, but for solving other problems -- could go toe-to-toe with a well-planned fighter, say, but that's not the point.
Take my bard/druid, Zeoll. Lord knows he's no match in battle for the power-attacking-fighters and battle-mages in the group. But he is designed to be a seer, to find out stuff. As one arrow in his quiver of tactics, he used easy bard ranks to learn Terran, Auran, and Aquan -- so as a druid, he summons elementals, orders them off in their own language to scout, and understands their reports upon return. Even a small earth elemental, for example, can walk through stone walls and floors! That's a great synergy for getting info. The point is, I really enjoy surprising my fellow players with answers to problems that they have no clue how to solve.
And the icing on the cake, for a truly well-rounded power gamer, is to make your optimized collection of feats and levels into a fully realized, three-dimensional character. How did your Divine Trickster convince the assassins' guild to reveal its secrets? Why is your Explorer-Merchant so fixated on finding new trade routes? Push beyond spell choice and skill ranks, and your character can join the ranks of heroes remembered for years and decades to come.
But let me not be too disingenuous. Dungeons and Dragons is a combat game, and most of its problems are best answered with force. The great majority of power-gaming strategies out there are combat strategies. But even so, the greatest war-machine PC is greater still with an engaging back-story and a winning personality.
Obsessive readers of my blog may have noticed that I group my screeds into three main themes -- (1) my own thoughts on D&D rules (Book screeds), (2) comments on game-oriented topics around the Web, with links (Click screeds), and (3) wemic- or feline-related posts (Lion screeds). Well, this is my 50th Book screed -- hence the philosophical cast to today's rant. Thanks for your kind indulgence! Here's to the next 50 ... and beyond!