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I know that in Power Grid a player can choose to save resources to power fewer houses, however are players allowed to build more houses than their total power plant capacity?
For example, suppose the total number of houses I am theoretically able to power with my current power plants is 5 (assuming that I have the correct resources and choose to power all of my plants), can I build a 6th house?
Your power plant capacity has no bearing on the size of your network. So you can build as many houses as you can afford. From the rules:
A player may connect to any number of new cities in a round, as long as he can pay the building and connecting costs.
Of course, it's probably a bad idea to build a network substantially larger than you can power. Balancing power plants, resources and network size is the key to the game!
Power Grid is a push and pull game. In some rounds, you grab a new station, and find yourself short on money for resources and houses. This may also mean that the next round, you will face lousy prices for both of these, too. In other rounds, you may have received a nice cash flow from those new power stations, and can indulge into the new houses as you don't need to spend another 20-30 coins on a new station for a couple of rounds, and can concentrate on the network or getting more resources.
Sometimes, it may be a good idea to stash some money and be the first one to break into Phase II and build the best second houses with no connection fees. This means you would need to have some 50 free coins to do that, so you may have to plan for it by building the power station capacity beyond 7, and bunking extra coal to fire up as many houses as you could -- basically, only buy houses on that turn.
