There are two accounts, both given by Diogenes Laërtius.

The first is much less interesting, in which he drank some undiluted wine, became very dizzy, and died soon after.

The second is the joke, and quite ironically he was laughing at his own joke! Laërtius recounted that while watching a donkey eat some figs, he exclaimed "Now give the donkey a drink of pure wine to wash down the figs!" and died in the subsequent fit of laughter.

Not a very good joke to die to, I'd say.