If this is a Whirlpool washer, most Whirlpool agitators are a split design (two sections). The top half is known as the "auger", while the lower part is the agitator. Between these two halves is a small cam assembly which is used to drive the auger, and an agitator bolt which holds everything together.
The problem you may be experiencing can be caused by a worn cam assembly, worn agitator dogs or a loose agitator bolt. The following link explains what agitator dogs are and how to access them:
If only the auger is loose, I would suspect the dogs or cam assembly need to be replaced. The part number for the dogs is included in the link I provided. For a little more you can purchase the entire cam assembyl which includes the dogs, the cam, the cam seal and thrust bearing.
If the entire agitator is loose, check the agitator bolt to ensure it is tight. DO NOT overtighten as this can restrict movement of the agitator or damage it. Tighten until snug.
Replacement parts can be purchased at any of the following websites:
All these sites are reputable and offer great service with competitive pricing, so shop and compare. The first three sites I listed also include helpful exploded view parts diagrams to assist you in locating and properly identifying the parts you need. If you do not wish to order parts on line, use the part numbers from the Sears website and go to your nearest appliance parts retailer. The agitator parts are commonly sold as part of their in-store inventory.
If you have any questions, please post back with a MODEL NUMBER (located on a nameplate along the wash tub rim under the lid), so that I can provide you with better assistance. I hope this helps you.