Is it possible to control an aircraft on the runway if the nose gear collapses?
Most aircraft are steered on the ground by pivoting the nose gear. If the nose gear collapses, you therefore lose your primary method of directional control on the ground.

Additionally, parts of the aircraft contacting the ground that are not supposed to contact the ground can cause unwanted yaw, which can contribute greatly to the runway excursions you've noticed in articles regarding gear collapse incidents. This is probably the largest contributing factor to runway excursions in cases of nose gear collapse. However, if it's known that the nose gear did not deploy properly before the landing, the pilots can intentionally hold the nose gear off the ground as long as possible in order to minimize this effect. Holding the nose gear off the ground as long as possible minimizes the time that the contact between the nose and runway surface will be potentially applying yawing forces to the aircraft and also minimizes the speed of the aircraft while those forces are being applied. This gives the pilots more time to respond with differential braking and/or rudder, helping to prevent the nose from moving too far away from the direction of travel and a resulting loss of directional control due to skidding. Of course, this doesn't help if the gear collapse was unexpected, as the pilots wouldn't know to hold the nose gear up.

There are a few additional methods of directional control available to airplanes on the ground, though most are not as effective as pivoting the nose gear and their effectiveness varies with speed:


Rudder - While the aircraft still has high airspeed when rolling down the runway, the rudder will still provide some directional control. This control will diminish very rapidly as the aircraft slows down, though.
Asymmetric braking - Most airplanes allow the pilots to control the brakes on the left and right main gear independently, allowing them to brake harder on one side of the aircraft than on the other. This is more useful for taxi speeds than for high speeds down a runway, though, and can easily cause even more directional control problems if used without proper care at high speeds.
Asymmetric thrust - Multi-engine aircraft almost always allow the pilots to control the thrust (either forward or reverse) of each of the engines independently. However, in the case of a collapsed gear, this is unlikely to be very helpful, due to the large delay between when a thrust change is commanded and when it happens as well as that the engines may now also be striking the ground themselves.