I keep a golf towel clipped to the cupboard right above the sink. It is reserved exclusively for wiping my hands after I wash them.
I keep a small bath-towel hooked over a drawer handle so it is readily available for drying dishes and cleaning up spills.
Car towels (there must be a name for them) work well too. I purchased a large pack at Costco. They are white and are meant to clean your car but they double as side towels too.