Should I Replace “Said” with Synonyms?

One topic that gets debated quite frequently in writing is the question of whether writers should use the word "said" or choose a synonym for the word. Any piece of writing with character dialogue has to deal with this question, and there's really two camps that stand their ground fervently. On one hand, English teachers tend to absolutely love when synonyms are chosen instead of the word "said" repeated ad nauseum. On the other hand, most successful literary authors, tend to use "said" more than any other word when describing a character talking. But there are notable exceptions. Which is right?