Drop test:

Lift the front wheel of your bike up about 6 inches of the ground.
Drop it and let it bounce. If the fork makes a stuttering sound it's
most likely a loose head set.

You say it's an old bike?
Either be cheap and just tighten your headset.
Or be nice and repack your headset with new
bearings and lots of grease. Tighten it to the point
where you can steer freely from side to side and
when you do the drop test it doesn't stutter.

People have mentioned loose brakes, crappy brakes, and loose cones. All of which are valid.
Everything must be tight and greased! EVERYTHING!!!!!!!!!!!!