If you don't have a will, your home state will distribute your wealth equally to your closest relatives, even if one is the richest person in the world and another is a pauper. A will gives you the ability to consider how much someone needs your property and/or how generous you want to be to a specific person.
A will also allows you to give away property in other than the fractional shares that would be dictated by your state's probate rules. In fact, you don't have to divide by fractional shares at all. You can give specific dollar amounts, make specific bequests ("2,000,000 shares of GM stock, " or "my collection of silver-plated spoons from the Millard Filmore memorial"), or set the amount of the transfer by a mathematical formula. (Such formula bequests are often used in connection with plans to minimize federal estate taxes.)