Is a Road Bike Faster Than a Mountain Bike?

In a word. Yes.

Road bikes are much faster than a mountain bike, it's pretty unusual to see a mountain bike overtaking a road bike. So, why is a road bike faster?

Aerodynamics - Road bikes have drop bars which allow you to adopt a much more aerodynamic position.

Weight - Road bikes generally weight a lot less. They have less suspension (i.e. none), the wheels are thinner and much more aerodynamic.

Tyres - Road bike tyres are usually around 25mm. This decreased rolling resistance makes a BIG difference to overall speed.

Fitness - Mountain biking and road riding require two completely different kinds of fitness. If you've never been on a road bike, you'll be surprised how it seems like harder work (cardiovascularly speaking). You just don't stop on a road bike, mountain biking can be more start/stop and using your core muscles.

FAQ

Q. How much faster are we talking?
A. Generally speaking, 3-5mph once you're used to the different style of riding a road bike.

Q. I've overtaken road bikes before. Am I awesome?
A. Possibly, possibly not. Roadies can often ride for 100+ miles, so maybe you're catching them on the way back and they don't care. Or you're awesome, take your pick ;)

Q. What can I do to speed up my mountain bike?
A. Fit slick tyres. Make a massive difference. Oh, and get fitter as that will make the most difference.

Q. So road bikes are better?
A. Nope. Road bikes are great fun, but so are mountain bikes. Pick the one you think you'll use.

Q. I can't make my mind up, what should I get?
A. Mountain bike. You can take your mountain bike on the roads, but you can't take your road bike on the mountain.

Q. Do I have to wear lycra?
A. No. Wear what you're comfortable with. However, who cares what you're wearing.