For a hand-picked selection of brain teasers across easy, medium and fiendish levels, have a look at the adult puzzle range at brain teaser puzzles.
For the big family session, party and bluffing games carry the day. The Traitors board game and card game, both available from The Happy Puzzle Company, work well with a larger group because they turn on reading each other and keeping a straight face, which suits the after-dinner mood. Keep one of these back for the moment when everyone is round the table and looking for something to do together.
Part of what makes it work is the head-to-head option. Two players each take a grid, roll the same starting positions, then race to finish first. A single round takes only a few minutes, which makes it easy to fit in before dinner or on a rainy afternoon. It suits ages six and up, and adults tend to get just as competitive as the children.
For gift ideas sorted by age band, with the number of players and rough playing time listed for each, browse the games-by-age pages at puzzles and games.
These games are a good pick if you want screen-free play that travels well and does not need a long rulebook. You can compare the full Genius line-up and read how each version plays at brain teaser puzzles.
It is worth thinking about the setting too. Games with a drawstring bag or a tin survive being thrown in a rucksack better than a large flat box. For a caravan or a beach hut with limited space, pick a few small games rather than one big one, so you can match the game to the mood without taking up a whole shelf.