General synonyms:
* Wordplay
* Play on words
* Witticism
* Jingle
* Double entendre (when the pun has a sexual or suggestive meaning)
* Quip
* Repartee
More specific synonyms:
* Paronomasia: A pun that uses words that sound alike but have different meanings.
* Antanaclasis: A pun that uses the same word with two different meanings.
* Syllepsis: A pun that uses a word that applies to two different things in a sentence.
* Homophone pun: A pun that uses words that sound alike but are spelled differently.
* Spoonerism: An accidental pun that involves switching the first sounds of two words.
The best synonym for "pun" will depend on the specific context and the type of pun you're describing.