Some games that go over well with teenagers at the monthly community board game nights that I co-host in my community have included:

Pandemic - A cooperative game where all the players play different riles within the CDC as they try to work together against the game to defeat global disease outbreaks.

Forbidden Desert - Another cooperative game where the players are a crew of adventurers who have crash landed in an ancient city that is being buried by a sandstorm. They have to work together against the game to recover and assemble the necessary parts needed to repair a flying machine and affect their escape before they are buried alive or die of thirst.

The Resistance - A social deduction game where players are members of the Resistance fighting to bring down a common enemy. The only problem is that a few of them are spies sent to sabotage their mission. They spies know who each other are and can more easily work together. It is up to the Resistance to ferret them out before it is too late.

Summoner Wars - A two player strategic card game in which two wizards summon forces to do battle with each other across a map. There is a great mix of factions and the simple ruleset combined with the asymmetric faction powers leads to a lot of interesting emergent properties in the play of the game.

Zombicide - Basically, it is Dead Rising the cooperative board game.

Rampage - A dextexerity board game that is largely influenced by the classic video game. You flick discs to move your Kaiju monster. You drop your large wooden monster on buildings to destroy them. You blow on buildings to shoot people out of each floor of skyscrapers or a football stadium. You flick wooden cars off the heads of your monster's pawn to simulate throwing them at buildings or other monsters for even more destruction.

Escape From The Aliens In Outer Space - A hidden movement game where haklf of you are scientists and the other half are mutants on a derelict space station. The scientists have to try to sneak to one of a number of airlocks that may or may not be functioning before being caught and eaten by the mutants. The trick is that you don't know which players are scientists or which are aliens and all your movement is secretly plotted on your own blueprint of the space station. Some spaces are safe zones. Others require drawing event cards. If you are lucky, no sound is detected. If you're slightly less lucky, a sound is heard somewhere else in the space station and you get to announce it; maybe your there and maybe your not (hopefully it throws off the mutants in pursuit). If your really unlucky, you make a sound at your coordinates, but hopefully you can bluff it so that the aliens think you aren't actually there. Teenagers LOVE this game and you can play with up to eight players at once. Its fun to watch a large group of teenagers play this together as you can watch it change their concept of what a board game is before your eyes.

Pitchcar / Roadzters - Wooden (or plastic, respectively) track dexterity racing games where your car is represented by a wooden disc (or plastic ball, respectively) that you flick around the course. The first to finish a prescribed number of laps wins. These games a lots of fun and always draw a crowd of spectators.

Small World - A "dudes on a map" light war game like Risk, but way more fun. Each faction is a random pairing of a trait like "seafaring" or "flying" with a race like "giants" or "skeletons". You do your best to control as much of the board as you can for as long as possible. When you can no longer hold out, you put your current faction in decline where ispt still earns points, but not as much and pick a new pairing that you think will help you hold the most ground.

Telestations - Combine Pictionary with Telephone and you get this game that's really,more of a gaming activity. Each player gets a random clue that they have to illustrate and then pass to the left. The next person guesses apwhat the drawing is and writes it as the next clue before passing to the left. At which point the next person illustrates the most recent clue. Wash, rinse, repeat. I've seen the clue "Bar of Soap" morph into "War of the Worlds." This is another that pre-teens and teenagers love and is only made better by people who are terrible at drawing (so most of us).

Dixit - Kind of like Apples to Apples, Dixit is a game where players hold a hand of surreal paintings. One you turn, you choose a card and make up a short story or say a phrase or word that you associate with it. Then all the other players choose amcard from their hands that they think matches your spoken clue. You all place the cards face down in the play area and then mix them up before turning them over. Then each player (other than you) votes on which one they think is the card you put down. If all the players or none of the players choose your card, you earn zero points; you clue was either too obvious or too obscure. Otherwise all the players and you score three points if they chose your card and every other player whose card was also chosen scores one point.

Neuroshima Hex 2.0 - Mad Max meets the Terminator, the abstract tactical puzzle game. Take one of a group of assymetric postapocalyptic gangs represented by a stack of hex tiles and try to figure out how to destroy the other faction bases using a combination of skill, luck, and timing, before they destroy yours.

Kill Doctor Luck, the Deluxe Edition - Think of this game as Clue's evil prequel. You're all stuck in a mansion with Doctor Lucky, an old coot that you all hate for some reason or another. You want him dead and you want to be the one that does it. The trouble is that he a slippery sun of a gun and it is incredibly hard to pull off the deadly deed without getting caught so you have to find a way to get him alone and out of direct eyesight so that you can try to kill him with whatever is on hand from "a killing joke" to "bad cream" to "a tight hat" and more normal fare like "a dagger", "a candlestick," and a "gun." Kids like this because they think it is subversive; they feel like they are getting away with something. If you like this one, make sure to check out Save Doctor Lucky, a prequel game where you have to make sure that Doctor Lucky survives the syncing Titanic so that you can kill him later.

These should get you started. In general a lot of the kids that come to our monthly board game nights like either direct confrontation games like Risk Legacy, Summoner Wars, Neuroshima Hex, and Small World where they can try out one upping each other in playful ways or the like cooperation games like Pandemic, Ghost Stories, Forbidden Desert, Shadows Over Camelot, and Zombicide; the harder the better. Kids love the challenge, but don't feel on they are on hook for any one decision as they can get input from the other players.

Good luck.