Catan is a family strategy boardgame for 3-4 players (previously called "Settlers of Catan"). It has a clever modular board that is arranged differently each time you play. Catan has inspired many different 3D versions; the board represents an island with 6 different terrain types, so it is the perfect game to model, be it out of resin or cupcakes. Searching the wider web will reveal literally dozens of versions, many exquisitely modeled, and even a commercial version which sold (originally) for over $300. OK, Catan is hardly chess, but it's off to a decent start.
Note: I've written a strategy guide for the game if you're interested in learning how to play better.
The board described here was made from scrap plywood, wood glue, inexpensive acrylic paint and some leftover polyurethane.