Adage = a saying that sets forth a general truth and that has gained credit through long use, a condensed but memorable saying embodying some important fact of experience that is taken as true by many people

Byword = A proverbial expression; a proverb, a condensed but memorable saying embodying some important fact of experience that is taken as true by many people

Saw = A familiar saying, especially one that has become trite through repetition

Proverb = A short pithy saying in frequent and widespread use that expresses a basic truth or practical precept, a condensed but memorable saying embodying some important fact of experience that is taken as true by many people

Maxim = a saying that widely accepted on its own merits
Axiom = a saying that widely accepted on its own merits