I bet you or someone in the household has long hair!
Get a wire coat hanger and straighten it out. Form a hook shape one end that is small enough to fit through the grate of the shower drain. Now insert the wire some 6 inches or so and twist around inside. When you remove the wire through the grate, you will pull back any hairs that have congealed with soap/shower gel causing the blockage. Remove these and you should be good to go.
A word of caution, this is not recommend for the weak stomached, the smell can be off putting.
Mike, January 2005