Tsuro is a popular board game in the more traditional style -- although not in the sense of Monopoly and Life. Tsuro is a last man standing puzzle/strategy game in which players build the board together, in hopes of being the last one to fall off the edge of the playing field.
The Tsuro board is a large 6x6 grid on which players take turn placing tiles. Each tile has a tangle of paths, connecting on each side to all adjoining tiles. They player starts at one edge of the board and lays tiles in front of them, each turn advancing by at least one tile, for as far as the path ahead of them will allow. As the game advances tiles start to connect, and the path will loop and twist over adjoining pieces. It does not matter how far you travel during your turn, but if your path ever reaches the edge of the game board you are out. The game ends when all but one player is out.
As the board contains only 36 spaces, eventually everyone would run into the border; the game is limited to 35 turns at most, as on the 36th turn every pathway is completed, and all paths end at the edge of the board. This means that most games, whether 2 player or 8 player, will not last longer than 15 minutes. Because every tile is designed to 'fit' in any orientation, this is a very simple game to play; you will not win if you just plop down tiles at random, but as long as you follow the rule that your next tile touches your current tile, you will progress apace. The makers recommend this game for ages eight and up, although I suspect that most 8-year-olds will not find the game too engaging after the first few playthroughs.
One pleasing aspect of Tsuro is the motif; the conceit is that this is a traditional Japanese game (it is not), played with stone markers on ceramic tiles. It is, of course, made of plastic and cardboard, but the aesthetic is still there, with muted colors, comparatively hefty game pieces, and a simple aesthetic. You can see the game, and learn more, here.
Tsuro has two expansions, Tsuro of the Seas and Veterans of the Seas, which have larger boards (7x7) and randomization factors. Additionally, the Star Wars themed Asteroid Escape is essentially the same game, redesigned with spaceships.