Ages 8 - 10
These are cards that have math problems on one side and the solutions on the other. These cards have several things going for them: The problems on them are the right ones (not trivial, not too hard, and teach worthwhile things). The cards themselves are colorful and artistic. Each card presents just one problem. Furthermore, all the kids I gave them to liked them.
Ages 8+
Set is an excellent game. It does not really teach anything specific, but it forces you to accelerate your brain, and it's great fun!
Ages 7+
An excellent puzzle game. Colorful
enough, and simple enough at the low levels, to be interesting even
for young children, yet, at hardest, difficult enough to be
challenging for adults. Develops planning skills, since it is
necessary to look ahead to find the solution. This game has numerous
equally interesting expansions and variants, shown on the right:
Rush Hour Game - Blister Pack 2 
This is a reasonably colorful and cute version of the standard peg solitaire. Said solitaire is a worthwhile game to play because it requires planning and strategy to achieve victory.
Starting from 10 years old
Fluxx is a very unusual game. The cards in the game create new rules. The rules and winning goals change all of the time. It is unclear how to strategize in this game. The amazing part is that I know people who have strategies and ideas in this game, so they can win more often than a random player.
Starting from 10 years old
Settlers of Catan.
Settlers of Catan is a fascinating board game. One of my sons played it in his dorm every day for 4 years. You do not get tired of this game. People who win in this game not only understand strategy and reasoning but also have amazing persuasive powers. People who like this game the most usually want to feel their power over other people. The rules are easy, but not too easy: when I first played this game, I did so without using the developement cards. This was because it was a little bit difficult to grasp all the strategy ideas otherwise. There is an expansion set
Starting from 10 years old
Ticket to Ride Europe
Ticket to Ride Europe is my favorite board game. The rules are easier than in "Settlers of Catan". There is no trading. The developement of the game depends on initial ticket distribution. Some strategies work sometimes, but other times, they do not work. You have to adjust your strategy to other peoples' moves.
There is another interesting version of this game that is called Ticket to Ride Marklin
For high school children preparing for math and programming competitions and adults
Ricochet Robots
Ricochet Robots requires seconds to learn and extreme brain processing power to play. Essentially, you have to calculate the shortest path algorithm in your head. Playing with one powerful person in a group might be intimidating. At the same time, it is great practice for rusty brains.