The idea that players should work together for a common goal is a new one in board games. Often, these games are HARD, because a game system needs to be designed to overcome the clever natures of its players. Fortunately, many brains are better than one!
Forbidden Island - Your team of adventures are exploring a rapidly sinking island, trying to get four artifacts off and escape before your trapped. If you are new to gaming and want a cooperative experience, this is probably the best introduction you can find. 30 minutes. 1-4 players.
Ghost Stories - You are a group of Buddhist monks defending a town from a horde of rampaging ghosts led by an incarnation of Wu-Feng. This game is unrelenting, but incredibly rewarding. 60 minutes. 1-4 players.
T.I.M.E. Stories - This is the sort of game Boards and Bites was built for. In this series of cooperative adventures, your team 'quantum leaps' into the past to try to make time go right. If you fail, go back to the start and try again. However, each story is a narrative experience you can only really play once, so make sure to get your friends together to play through each time to avoid spoilers! 90 minutes. 2-4 players.
Arkham Horror: The Dunwich Encounter
Arkham Horror: The Yellow King
Assault on Doomrock
Assault on Doomrock: Doompocalypse
Attack on Titan: The Last Stand
Betrayal at House on the Hill
Betrayal at House on the Hill: Widow's Walk
B-Sieged: Sons of the Abyss
Legendary Encounters: Alien Deckbuilding Game
Legends of Andor
Mansions of Madness
Mountains of Madness
Shadows Over Camelot
Sherlock Holmes Consulting
Star Trek: Frontiers
The Big Book of Madness
The Captain is Dead
The Lost Expedition
TIME Stories: A Prophacy of Dragons
TIME Stories: Expedition: Endurance
TIME Stories: Lumen Fidei
TIME Stories: The Marcy Case
TIME Stories: Under the Mask
Tiny Epic Defenders
Unlock! Squeek & Sausage
Unlock! The Formula
Unlock! The Island of Doctor Goorse
XCOM: The Board Game
Zombicide: Black Plague