Having a will does not avoid probate. In fact, a will is actually a tool of and for the probate process, one purpose of which is to carry out the intent of a deceased person. Therefore, prior to death a person indicates his or her intent in a document which is referred to as a will.
Probate, however will generally involve costs, publicity and delays which some people would prefer to avoid. In those cases other estate planning techniques can be used to good effect.