ScarletRose: A record chess game between Nikolic - Arsovic (Belgrade 1989), with 269 moves.

Chess is infinite: There are 400 different positions after each player makes one move apiece. There are 72,084 positions after two moves apiece. There are 9+ million positions after three moves apiece. There are 288+ billion different possible positions after four moves apiece. There are more 40-move games on Level-1 than the number of electrons in our universe. There are more game-trees of Chess than the number of galaxies (100+ billion), and more openings, defences, gambits, etc. than the number of quarks in our universe!

The longest Chess game theoretically possible is 5,949 moves.

for more, see the fs ;)

It's unlikely that a chess game would go over 100 or even 75 for that matter. But I've played many games that neared the 75 mark.