No matter how careful or professional you are when painting, it's inevitable: you're going to get paint on something you didn't intend to. If you get paint on a favorite polar fleece sweatshirt or blanket, chances are you can clean it off even after it has dried using materials you have in your house already. If not, there are some products available that can remove dried paint from fabric quite well.
Identify the type of paint. Water-based products won't remove alkyd (oil-based) paint, and mineral spirits will have no effect on latex (water-based) paint.
Saturate the paint stain with mineral spirits if it's wet alkyd paint. Using a clean cloth, blot the polar fleece, re-wetting as necessary and turning the cloth, until the paint is absorbed. Then wash the fleece in cold water and detergent.
Rinse the fleece in water if the paint is water-based and still wet. Hold the painted area under running water, if possible, turning and squeezing until the water is clear. If you can't do this, saturate the paint with water, then blot and re-wet until the paint stain is gone.
Try very hot water on dried paint. This can work if the dried paint is still fresh because it will soften fresh paint. Either soak the fleece in hot water, then blot and rub it until the stain is gone, or saturate the stain with hot water, then set a towel soaked in hot water over it.
Pour rubbing alcohol over the paint stain, blotting it with a rag until the paint is removed. Rubbing alcohol also softens dried paint.
Scrub the paint gently with a soft brush (even a toothbrush will do) if it's penetrated the fibers to the back of the fleece. While the paint spot is saturated with your cleaning agent, comb through the fleece fibers to remove the small shreds of loosened paint.