One notable, annual, repeated chess game is played at the Marostica Chess Festival, which commemorates a famous chess game played between Rinaldo d'Angarano and Vieri da Vallonara for the hand of a maiden in 1454. A nice duel. Not quite as violent as the gun or sword duels that were more common.
I am uncertain as to the source of the following game. I have obtained it from [http://www.chess.com/blog/OldChessDog/human-chess-game-at-marostica/]. It claims to be, in the PGN header, from 1454. However, since I cannot verify this, I believe that it is the game from the 2014 Marostica chess festival. Apologies for the uncertainties. It is, however, a cracking game, so I’ve included it.
Actor Playing Rinaldo d'Angarano(?)–Actor Playing Vieri da Vallonara(?) Marostica 2014(?)
The following game was obtained from http://humanchess.typepad.com/lowereastside/. It was, evidently played on a largish grid of city streets, with each intersection a square. Above is a story on what it was like to be a Black knight.
Jennifer Shahade-Gregory Shahade 2004
The following is, sadly, an honorable mention. Kasparov-Timman was, however, played in a very cool way: with shipping containers as pieces in an effort to promote the shipping company APL. They are, as described below, believed to be the largest pieces ever used in a chess game.
More info: http://www.prnewswire.com/news-releases/apl-sponsors-worlds-largest-chess-game-during-rotterdams-celebrations-74295892.html
Garry Kasparov–Jan Timman Wereldhaven Festival 1999