Yes, cotton shrinks in the wash.

More Info: When fabrics are manufactured they are placed under continuous tensions causing them to stretch-this is especially true of cotton.  When these same fabrics are then placed in water, either hot or cold, the fibers of the fabric begin to relax releasing the tension that caused the stretching action.  This causes the garment to shrink.

How to Prevent Cotton Shrinkage

Treatments such as Sanforized® can be added to a garment during manufacturing that can help to reduce shrinkage.  Sanforized® is a trademarked name for Controlled Compressive Shrinkage, where fabrics are pre-shrunk by compressing wet fabric, stretching it through a pressure zone, and drying it.  These fabrics are tested for shrinkage before they are made into garments.

Tumbling Shrinks Cotton not Heat?

According to Cotton Incorporated, the research and marketing company representing a portion of the US cotton growers, an informal study demonstrated that it is not the heat of the dryer that is to blame for your cotton garment shrinking, but the tumbling action.  Researchers placed cotton garments in a dryer with two different low heat settings and found that the garments in both cases shrank by 20%.  They then set the dryer to have no heat source and found that the garment still shrank by 20%. Following the findings, the company recommends that for best results, tumble your knitted cotton garments for no more than five minutes to remove the wrinkles, then remove and hang to dry.