More shapes! Here's a hexagon, from Settlers of Catan -- one of my favorite boardgames.
As you may (or may not!), I'm something of a boardgame geek. Not Monopoly, Life, and things like that -- boardgames have come a long way! This game, Settlers of Catan, is often credited for helping to popularize the modern boardgame. It's an example of a "eurogame" (as in, from Europe), one which tends to be based on strategy, indirect competition (usually for limited resources), and aimed at adults as opposed to children.
Settlers is fairly simple. Each game, you place a variety of hexagons (some shown here) into a grid, and place certain numbers on them. The hexagons represent resources, which you can use to build and expand your empire. The numbers represent die rolls -- you can only earn resources when the die rolls your numbers! The other pieces are settlements and roads, which you build to gain points (and to access new resources).
If you're interested in more, check out the Settlers link above. It goes to a description of Settlers on an excellent site called BoardGameGeek, which is something of a boardgaming Mecca. Enjoy!