No. Most states allow a certain amount of property to pass free of probate or through a simplified probate procedure. In California, for example, you can pass up to $100,000 of property without probate, and there's a simple transfer procedure for any property left to a surviving spouse.
In addition, property that passes outside of your will -- say, through joint tenancy or a living trust -- is not subject to probate. For a discussion of the most popular probate-avoidance methods, see Nolo's article How to Avoid Probate.