As someone who really enjoys narrative board games, I really recommend
Dead of Winter by Plaid Hat Games and
Fallout: The Board Game from Fantast Flight.
Dead of Winter is a co-op, psychological narrative horror board game set during the zombie apocalypse where you have to work together to manage a small colony of survivors holed up in an abandoned warehouse. Each player controls their own party of survivors and has to take care of their needs, supply them, send them out to scavenge for goods, and clear an ever-growing presence of the undead. Where it really shines is the "Crossroads" system, where at the beginning of each players turn one player secretly draws a card, and if the conditions on the card are met it triggers a story beat, and the player whose turn it is will either have to make a decision that heavily impacts the game, or the colony will have to vote on it as a group. There's also a mechanic where one player's group of survivors can be secretly working against the colony to further their own nefarious goals, and the rest of the players have to track them down in a closed space a la The Thing. Makes for some fantastic moments.
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Fallout: The Board Game is a really unique board game in that it's a simplified, explorational turn-based RPG that acts as a super-faithful love letter to the series. You start with a unique character with limited supplies, and over the course of the game you complete quests, level up, fight mutants and bandits, make narrative decisions, roll for dialogue and skill checks, complete storylines, gather money, equipment, and weapons, and try to complete enough challenges to beat the game by the time the scenario's ticking clock runs out. The nice thing about it is that since every person can win or lose the game independence of one another, you're free to either work against the other players or with them, forming groups to clear dens of mutants and bandits or even luring them towards your opponents. While the game is littered with references to the modern video game series (and even the original two games if you have the relatively cheap New California expansion), I've played it with friends who've never played the series and they enjoyed it just as much because it's really well put together.
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