Blokus

  Blokus was fun to play right out of the box. The directions are simple enough to be playing within a minute. Learning how to play the game well takes longer.
  Each person has colored tiles connected in different patterns. These tiles must be laid down corner-to-corner with the same color. Players try to block each other and leave themselves enough space to play all their pieces.
  We found that if two players use one color each, it's too easy. If two players play two colors each, it's a game that is as challenging as a four-person game.
  Young children will enjoy the colorful tiles that look like jewels. Older children will enjoy mercilessly blocking off their parents. Blokus has won many awards, and I can see that the game has educational value, teaching spacial relationships and logic. The education isn't heavy-handed, however, and Blokus is a fun, competitive game that takes about 20 minutes to play.
  For ages 5 to adult, 1-4 players. Cost: About $25.

Our rating: 4 out of 5 stars

Othello

  Othello is another one of those logic games that doesn't take too much time to learn or play. I like that my toddlers have enjoyed playing with the pieces, which are smooth and feel nice to place in the velvety squares. The chips could be a choking hazard, so supervise small children.
  This game is easy to handicap, too, for example by giving a younger child a couple of corners right from the start. If you give them all four corners, good luck, because they'll probably win no matter what you do.
  The game is played by turning over the chips again and again as each player puts down a piece so that his color is on either end of the opponent's color. The rules take some explaining, but are logical and easy to understand. As the box says, "A minute to learn ... a lifetime to master!" That's trademarked, y'all.
  We've had some emotional outbursts playing this game with young children. Something about having all their pieces turned over to the other color is upsetting. But it's another game I like for its simplicity and short play time.
  For ages 8 to adult (or younger if you're not using rules), 2 players. Cost: About $12.

Our rating: 4 out of 5 stars

Master Mind

  Master Mind has changed what it says in its box. My old version says "Easy to learn. Easy to play. But not so easy to win." Nowadays, it says "The Classic Game of Logic and Deduction." The change is appropriate because although this is one of my favorite games, it is easy to win once you know what you're doing.
  But that's what I like about it. I know that if I think well enough, I'll win the game. I taught my son my strategy, and now he can win, too. It's not "easy to win," but you will win if you think things through properly.
  In Master Mind, one person hides four colored pegs. The other person tries to guess what colors they are, and in what order. If the guesser gets a color in the right place, he gets a black peg. If the guesser gets a color in the wrong place, he gets a white peg.
  When I was a kid, my sisters and I figured out that it's good to start with your first three guesses being two colors each. You can use this information to guess the code in one or two more guesses if you're lucky. Usually, I guess the code in six guesses, seven if I'm unlucky.
  Master Mind is just the right level of difficulty to make you think but not get your frustrated. A game lasts about 10 minutes, so it's easy to play a couple times and be done.
  For ages 8 to adult, 2 players. Cost: About $12.

Our rating: 5 out of 5 stars

Black Box

  Black Box was made by Parker Brothers in the late 1970s and isn't made anymore. See the Wikipedia listing for a thorough explanation of the rules. I mention this because the game could be played on grid paper. Each of two players would use a piece of grid paper marked out to be an 8x8 grid. The "hider" marks four or five squares on the grid; pretend there's a ball in those chosen squares. The "seeker" tries to find these squares by pretending to send a laser beam into the grid. This laser beam bounces off the "balls" and then leaves the grid. By observing how this laser beam bounces, the seeker should be able to figure out which squares on the grid the hider chose.
  This is a good game for nonreaders, for kids who like to solve puzzles and for those who like logic games. The purchased game, which was mine as a kid, was cool because the box is black and the pieces are red, yellow and orange, so the contrast was interesting. The rules were unlike other games we had. The purchased game uses a crayon wipe-off grid for hiding the balls. This is something that could be useful for a homemade version of this game.
  For ages 10 to adult, 2 players. Cost: About $10 on ebay, or make your own game with grid paper.

Our rating: 3 out of 5 stars