Do you mean in a truly competitive game?
(Since collusion could produce a game thousands of moves long.)
In over the board chess, the longest game on record is 269 moves.
https://en.wikipedia.org/wiki/List_of_world_records_in_chess
/ This question is asked several times a month on chess.com. Knock yourself out:
https://www.chess.com/forum/search?keyword=longest+game
Among all the games ever played on chess.com, between two humans, which games has the most moves? What's the record? Anyone knows?