Does anyone know which is the longest game on the site, i.e. the game with the most moves?

There are not very long games.

Longest draw: #5370.

Not draw: #380

Does anyone know about famous very long games that has been played among the top players in the world?

124 moves

KORCHNOI/KARPOV: DRAWN by stalemate. Nimzo-Indian, Game 5, 1975 World Championship, 27-28-29 July, Baguio, Phillippines.

This is the longest game I know of between two grandmasters in a serious game.

The longest GM-GM game I have in my database is Murey-Rausis at the 1995 Philidor Memorial in Paris. It went 196 moves and ended in a draw. The longest non-draw was Short-Salov at Linares in 1990. It went 162 moves.

For other chess records, check out Tim Krabbé's wondeful “Chess Curiosities” site, located at:

http://www.xs4all.nl/~timkr/records/records.htm