Sunbeams are seen because of light scattered from water droplets and dust and smoke particles suspended in the air. If the cloud cover only has a few small holes in it, then parallel shafts of light will scatter light in all directions so you can see the sunbeams.
The light from the sun really isn't exactly all parallel because of the size of the sun. Some light rays come from one part of the sun and others from other parts, and these can have different directions. But for the purposes of your question, this effect may be neglected.
The reason you see the sunbeams converge is good old perspective -- the projection of an image of a three-dimensional object onto a two-dimensional plane. If you stand on a railroad, for instance, the rails will appear to converge the farther away you look, even though the rails are parallel. If two objects have the same distance from one another, then the angular separation between them decreases as the two objects are farther away.
The reason the convergence point is at or above the clouds is because the beams are farther away from you high in the sky than they are closer to the ground. It is conceivable that if you stand under the holes in the clouds and the sunbeams shine nearly parallel to the ground, then they will appear to converge as they go downwards, just as the rails do.
(republished on 07/29/06)