I don't do much.

I check the tire pressures at the beginning of the week and top them off. I clean and lube the chain maybe once a month (probably less), whenever I start to hear it straining or squeaking. I have replaced the chain once around 4,500 miles (6,000 miles on bike currently), and have replaced two rear spokes. Oh yeah, and a new set of tires about 1,000 miles ago. Other than that it has been perfect. I haven't even had to touch the shifters or the brakes!

I think a lot of the necessary maintanence depends on how far you ride, if your bike is kept outside, and how often it rains. Also if you have fenders, you probably won't have to clean the chain quite as often...