I've been meaning to post about this one for a while...
When I was a teenager, I worked as an 'Explainer' at Questacon. One of the science demos I was trained to do was a bit on gyroscopic precession: if you take a bicycle wheel, spin it, and then try to tilt its axis while it's spinning, it will pull around. And we were taught (and duly taught our visitors) that Gyroscopic Precession Is What Keeps Bicycles From Falling Over. It seemed sensible enough - after all, it's much harder to balance a bike when standing still than when it's moving and the wheels are spinning. And gyroscopic effects are what stabilises a number of other things - spinning tops, for instance. Indeed, if you detach a wheel from your bike and roll it downhill on its own, gyroscopic effects due to its rotation are what keeps it upright instead of falling over on its side.
Many, many reputable physicists tell us that it's the same thing with a bicycle, or a motorbike. Straight Dope, for instance, repeats the claim. But it's hard to argue with this:

http://www.losethetrainingwheels.org/default.aspx?Lev=2&ID=34
This wonder, created by Dr. Richard Klein of UIUC, is a zero-gyroscopic bike. The two airborne wheels are in contact with the two on the ground, so they rotate at the same speed but in opposite directions, cancelling out any gyroscopic effects. Despite this, the bike is still quite easy to ride. Before Klein, English researcher David Jones had published similar findings, and his article on his fruitless attempts to build an unrideable bike is quite entertainingly written.
So why do bikes stay upright? Wikipedia has a more detailed discussion, but it comes down to forward movement. When your bike starts to fall over to the left, steering slightly to the left brings the base of the wheels back under the center of gravity, restoring stability. Most bikes will steer into the direction of the tilt even without the rider's intervention or gyroscopic effects, due to their 'trail'; you can test this for yourself by tilting a stationary bike. But as the first link above discusses, even bikes with zero trail can be ridden quite easily as long as you keep your hands on the handlebars; hands-off, you can balance with the aid of precession, but it's not nearly as easy as balancing hands-on without precession.
When I was a teenager, I worked as an 'Explainer' at Questacon. One of the science demos I was trained to do was a bit on gyroscopic precession: if you take a bicycle wheel, spin it, and then try to tilt its axis while it's spinning, it will pull around. And we were taught (and duly taught our visitors) that Gyroscopic Precession Is What Keeps Bicycles From Falling Over. It seemed sensible enough - after all, it's much harder to balance a bike when standing still than when it's moving and the wheels are spinning. And gyroscopic effects are what stabilises a number of other things - spinning tops, for instance. Indeed, if you detach a wheel from your bike and roll it downhill on its own, gyroscopic effects due to its rotation are what keeps it upright instead of falling over on its side.
Many, many reputable physicists tell us that it's the same thing with a bicycle, or a motorbike. Straight Dope, for instance, repeats the claim. But it's hard to argue with this:

http://www.losethetrainingwheels.org/default.aspx?Lev=2&ID=34
This wonder, created by Dr. Richard Klein of UIUC, is a zero-gyroscopic bike. The two airborne wheels are in contact with the two on the ground, so they rotate at the same speed but in opposite directions, cancelling out any gyroscopic effects. Despite this, the bike is still quite easy to ride. Before Klein, English researcher David Jones had published similar findings, and his article on his fruitless attempts to build an unrideable bike is quite entertainingly written.
So why do bikes stay upright? Wikipedia has a more detailed discussion, but it comes down to forward movement. When your bike starts to fall over to the left, steering slightly to the left brings the base of the wheels back under the center of gravity, restoring stability. Most bikes will steer into the direction of the tilt even without the rider's intervention or gyroscopic effects, due to their 'trail'; you can test this for yourself by tilting a stationary bike. But as the first link above discusses, even bikes with zero trail can be ridden quite easily as long as you keep your hands on the handlebars; hands-off, you can balance with the aid of precession, but it's not nearly as easy as balancing hands-on without precession.