American Presidents retain the title President when they have left office. What of Vice Presidents? Nobody seems to call Al Gore 'Vice President' Is that at his request or is it not the convention ?
Yes, former vice presidents are often addressed as vice president X. Gore was addressed or referred to that way several times just this morning when he testified before congressional committees.
Since, before becoming Vice-President, Al Gore also served in the United States House of Representatives and the United States Senate, proper etiquette states that he has the title "The Honorable," for life.
As for the titles "President" and "Vice-President" after leaving office, according to Miss Manners the keeping of the title "President" after a President has left office is a "...violation of American protocol..." For reference, she points out:
Only holders of unique titles, such as president of the United States, are supposed to surrender them on leaving office. Former presidents Truman and Eisenhower gracefully assumed the last multiple titles they had held, senator and general respectively.
When addressing a former president of the United States in a formal setting, the correct form is "Mr. Last Name." ("President LastName" or "Mr. President" are terms reserved for the current head of state.) This is true for other ex-officials, as well.
When talking about the person to a third party, on the other hand, it's appropriate to say, "former president Last Name." This holds for introductions, as well: A current state governor is introduced as "Governor Tom Smith," while you'd introduce an ex-governor as "former Governor Jim Bell."
Now, let's wade a bit deeper. In an informal setting (such as a private lunch), it's acceptable to use the title the ex-official held. Here, you could refer to former president Jimmy Carter as either "President Carter" or "Mr. Carter."