If you are legally changing your name once you get married, you need to notify an array of authorities to make sure there's no confusion post-nuptials. The sooner you do this after you say "I do," the better. Some organizations require proof of marriage — A.K.A. your marriage certificate, which is issued after the wedding — so you'll want to have that handy, as well. If you and your new hubby are changing addresses, kill two birds with one stone and notify these organizations as well.
As you can imagine, the most important places you'll need to inform of your new name are the Social Security Administration, motor vehicles department, and your local passport agency. Next, think about work — you'll need to fill out the necessary paperwork with the payroll department at your office, and inform your banks of the change and have new cards and checkbooks issued to you. The same goes with any credit unions, mortgage companies, voter registration, and credit card companies.
Some lower-priority changes you might still want to make include any religious organizations you belong to, magazine subscriptions, and any accounts you hold at local stores. If you wish to, informing alumni organizations and doctors of the change isn't a bad idea either. Of course, you'll want your family and friends to know as well so that when they send you anything they'll know how to address an invitation or card (by the way, you should inform them if you're not taking your husband's name or choosing to hyphen your names as well — you don't want them to get it wrong!).