European swallow, that is. And the answer is (drumroll):
11 meters per second, or 24 miles an hour
So if you should encounter the Old Man from scene 24 on the Bridge of Death nearest you, you'll know. (Although it's much more fun to watch him go over the bridge).
For how that number was reached, check out this site:
Estimating the Airspeed Velocity of an Unladen Swallow by Jonathan Corum.
He even has graphics.