San Gimignano uses large hex tiles as a board, each showing three areas with one of four different colors. A start set of tiles are laid such that no color touches itself on an adjacent tile. Through the game, tiles are added to the board by the players with this same restriction.
On your turn, you add a marker to claim one of the colored spots on the board; up to two markers can be placed on a space. When you have four adjacent markers that are all on different colors, you can place a tower. Once the tower is placed, this spot is no longer usable for any other marker connections. The game ends when no more towers can be placed or when someone manages to place all 10 of their towers. The player with the most placed towers wins.
Tile placement and marker placement are both critical, as is where to place your tower so that you don't shut off further growth options. It is possible to end up with a bunch of uselessly placed markers once all four colors will not be available to any of them. The game nicely comes with English and German rules.
A note about the unusual material of the "towers" can be found in a Geeklist thread: