This problem is very simple, inexpensive and easy to repair.
Whirlpool manufactured washers use a split agitator design. The upper portion is called the auger, while the bottom is called the agitator. Between these components is a agitator cam assembly. This problem is commonly caused by worn agitator dogs or the agitator cam assembly. The following link explains what the dogs are and how to replace them:
http://www.fixya.com/support/r3608577-replacing_agitator_dogsThe part number is included in the link provided. You can purchase replacements at pcappliancerepair.com for about $5. For a little more you can purchase the entire cam replacement kit, which includes the cam, the thrust bearing, and the dogs for about $11 or $12.
NOTE: You can refer to the excellent exploded view parts diagrams the web site has to offer for assistance. Whirlpool also recommends the application of a little grease on the thrust washer. The part number for their recommended grease is AP3098553.
The special tool that you need to use to get the recessed agitator bolt off is a 3/8" to 1/2" rachet adapter. You can purchase one at any hardware store if you don't have one.
If you have any questions about this repair, please post back with your complete model number (located on a nameplate along the wash tub opening under the lid) and let me know. I hope this helps you.
NOTE: DO NOT overtighten the agitator bolt. This can cause damage to the plastic, or restrict the agitator movement. Tighten until snug only.