At what height should I have my seat on a road bike?
There are a number of ways to determine the seat height for a road bicycle. But you should also pay attention to how you feel while riding your bike at different heights. In addition, it is important to consider your entire position, not only the seat height. Finally, if you are riding a lot, change your seat height in small increments over time to avoid injury.

Here are some of the popular methods for determining seat height:


There should be some bend in your knee at the bottom of the stroke; 


your seat is too high if you should have to wobble your hips with each pedal stroke to reach the pedal.
Your seat is too low if your thighs hit your stomach  

Sit on the bike, put your heel on the pedal, and your leg should be fully extended. This provides a good starting point 
Another good starting point is Greg Lemond's recommendation from "Greg LeMond's complete book of cycling" states that the distance from the top of the seat to the center of the pedal should be 0.833 times the distance from the floor to your crotch, measured with your back and heels against a wall. If you use clipless pedals, subtract 3cm; 
if you drop your heels at the bottom of the pedal stroke, decrease the height and if you point your toes, increase the height  relative to these recommendations.
When you need more control (crit racing, urban cycling, bicycle polo) lower the seat; for more power (hill climbing, time trialing), increase the seat height.


Again, once you get these starting points, you can adjust until it feels right. I would also suggest getting a professional fit, especially if you ride a lot or are planning to purchase a new bike. Probably the most important attribute of a new bicycle is it's fit. A proper fit will do more for your riding enjoyment, skill, and speed than any component or frame material (excluding department store bikes).

Some good online resources include:

http://www.peterwhitecycles.com/fitting.htm

http://www.caree.org/bike101bikefit.htm

Here is a list of references found in the chapter on Body Position for Cycling from the book "High Tech Cycling" by Ed Burke. The entire book can be read at google books.