Abstract Strategy
Abstract strategy games feature that classic "easy to learn, hard to master" balance and are accessible to all audiences. What's more, new abstract strategy games mix up the usual "move and capture" formula of their predecessors. For example, Ingenious challenges teens to create color patterns to earn points. Games like Tile Chess take familiar games and add extra dynamics: imagine six-player chess without a board.
Roll-and-Move
Traditional roll-and-move games have a set board to move around. That gets boring fast. Many modern roll-and-move games feature boards players assemble as they play, while others add challenges like combat. For example, Zombies!!! casts players in the roles of survivors racing out of a zombie-infested city. Players must fight to stay alive and conserve ammo as they run for their lives. While playing your teen will learn about cost-benefit analysis -- with a little help from the undead to keep it entertaining.
Racing
Your 15-year-old may be itching to drive, so give him a game that lets him do just that. Modern racing games are built around strategy, not random dice-rolling. Some, like RoboRally, allow teens to not only race but smash up their opponents, just like in their favorite video games. The game teaches the rudiments of programming and design, all while making players blast each other to pieces.
War
War games hold instant appeal to most guys and require considerable strategic thinking skills. Collectible war games such as like HeroClix allow teens to hold battles between their favorite video game and comic book characters. But like collectible card games such as Magic or Yu-Gi-Oh, it takes a lot of buying to build a good army. Instead, start with stand-alone war games like Tannhauser, which features steampunk warfare between U.S. soldiers and Nazi demons. These can give your teen a taste of war gaming without requiring a heavy investment.
Role-Playing
If you want your teen to really exercise his imagination, encourages games like Dungeons &Dragons, which allows teens to rescue damsels in distress and quest for glory, all without ever leaving the living room. These games can sometimes be a challenge to learn. Board games such as Descent and Hero Quest are one way to introduce your teen to the genre.
Eurogames
Eurogames teach everything from history to economics, all while showing a players a very good time. Eurogames typically focus around acquiring resources and using those resources to build things. They also frequently involve role-choosing, where players choose special abilities each turn. Choosing the right role at the right time can be just as important as having the right resources. For example, in the award-winning Puerto Rico, players role play as colonial landowners. They must grow crops, build neighborhoods, sell produce and ship goods back to Europe. To do this, they choose roles like settler, builder and trader. One benefit to Eurogames is they avoid player elimination. Nobody gets killed off before the game is over, giving everyone a chance to win. This works well for competitive teens. Start with Settlers of Catan, a game where players colonize an island. They acquire resources like grain, wood and stone and build settlements, roads and cities. They even make war. Rules are simple, the replay value is high, and playtime is only an hour. The game is so popular it was adapted into a video game.