This type of grip is usually the choice of players who want a softer feeling comfortable grip. There is a choice of surfaces, and usually they are smooth or perforated.
Note: using an overgrip does increase the size of the handle.
Smooth or Perforated
Some players prefer a perforated grip, as they believe they provide better moisture absorption.
Tacky or Dry
A tacky grip is probably best for dry hands, and a dry surface usually provides more absorption.
Surface Pattern
A small number of overgrips have a patterned surface. This does not seem to have any real advantage, so it is probably more cosmetic than practical.
Some Grips: tested and recommended
Head
Xtremesoft
a tacky grip with large perforations for improved absorption.
Tecnifibre
Players Wrap
a white perforated grip that provides a good non-slip surface.
Wilson
Pro Overgrip
One (or two) of the best grips available. There is both a plain and a perforated version.