The most common problem people encounter with a Craftsman snowblower is that it invariably has damage to one of its parts, according to askville.amazon.com. The most likely culprits are the auger, a belt, or a shear bolt.
Some troubleshooting should help you identify the problem. Once you have pinpointed the part, it is often simply a matter of getting a replacement part. Since snowblowers are notoriously expensive to repair, it is worthwhile to inspect the machine regularly in order to spot wear and tear before it becomes a problem. Often the problem can be as simple as stale gas left in the tank in the off-season.