The most basic strategy in Power Grid is a balanced approach. You want power plants that can power as many cities as possible using as few resources as possible. You also need the resources to power your plants. Finally, you have to have cities to power. If you have plants that can power 11 cities, but you only control six, you won't be able to earn the maximum amount of money each turn. Similarly, if you buy access to 10 cities but your plants can only power four of them, you've wasted some of your Elektro.
However, particularly in games with four or more players, an aggressive unbalanced strategy can be effective. As the game goes on, access to cities becomes more and more expensive, and eventually players will be blocked out of cities entirely. If you purchase many cities early in the game, you'll spend less on them and force other players to spend more. Controlling a lot of cities also gives you some say on when the game ends. The last turn occurs whenever anyone controls his or her 17th city, so you can trigger this when you're in a position to win the game.
Later in the game, power plants tend to use more resources, so resources naturally become more scarce and expensive. Players have a limited ability to store excess resources, so it is difficult to "corner the market" on a resource and artificially manipulate its price. Multiple players can collude to drive up the price of a particular resource, or even buy out the entire stock. This can cripple a player who goes last during the resource buying phase (typically whichever player leads at the time).
The power plant auction phase is crucial. Wind-powered plants are highly sought-after and may be worth a premium price, but don't get carried away by a bidding war. They will often sell for slightly more than the amount of Elektro they would earn in a single turn. The most important thing to remember about the auctions is to avoid resource competition. If you notice that no other players are using garbage-powered plants, purchase one of those and you can get the garbage resource at a cheaper price. Make sure your own plants use diverse resources, too. You don't want to compete against yourself for resources.
Most importantly, keep an eye on the numbers. As someone gets close to controlling 17 cities, you need to make sure you've got enough resources to go for the win. Take a look at your opponents' power plants and check how many cities they can power. This will determine crucial late-game power plant and resource purchases. The last two or three turns, things can get pretty cut-throat around the Power Grid table!
- Rio Grande Games. "Power Grid." (Accessed August 3, 2011). http://www.riograndegames.com/games.html?id=5