My favourite game when I was little was Labyrinth (that word never looks right). We (my parents, brother and I) used to play it all the time. It was a logic sort of game. At the beginning, everyone gets dealt cards with pictures of various treasures on them, but you can only look at the first card. The board is a maze, made up of rows of tiles with different maze pieces on them (l-shapes, straight pieces, t-junctions, etc.). Every other tile in a row or column is glued to the board, while the others are loose and placed on the board at the beginning of each game. This allows every other row or column to slide, by inserting a free tile at one end and pushing the row until the last tile of the other end falls off, which is given to the next player to use for their turn. The goal is, by moving your man through the maze and using the tile to slide pieces favourable to your intended target, you land on the pieces with your treasure on it. Then you look at your next card and try to get to that one. And after all your cards are gone, you have to get back to the starting position. I hold the record of managing to get all of my treasures in one turn, through sheer luck.
There's a good picture of the game board here. The arrows are the rows that slide. It's funny, I remember that board being much bigger than it actually is. Probably because it was harder for me as a child.
We played that game until it got too easy for me (as the youngest member of the household), then we donated it to Value Village. But it was lots of fun and we always took it on vacation with us.