Games are a wonderful way to learn a whole range of subjects and are one of my absolute passions. They provide a great opportunity to interact in the real world or online, improve your mental agility and acquire new knowledge.
Even games that don't appear to be 'educational' in nature often help children (or adults) to learn the connections between things and to gradually develop skills, whether it's spatial awareness, forward planning, reading or a less tangible skill.
Competitiveness is a natural part of the world (look at evolution and the 'survival of the fittest) and I personally have nothing against it when it's in a game, however there's also plenty of room in the world for co-operation and indeed it's essential that people and nations learn to co-operate together more effectively for a whole myriad of reasons. Younger children are also often easily upset by losing or feeling that something's not fair (perhaps because an older sibling keeps winning) and while these are all part of life's learning experiences, it's great to have some co-operative games to play.
It's possible to turn many games into co-operative games by aiming for the highest TOTAL score of all players, rather than having a score each. For example, if you're playing Scrabble, then you can just have a single score and aim to get the biggest possible, for example, by opening up Triple Letter spaces for other players. Another co-operative version of Scrabble is that you can aim to finish the game as quickly as possible. Set a timer at the start of it, don't score at all and simply play as fast as you possibly can until the game is finished.
Carcassonne and other strategy game also have a good balance between co-operation and competition, as you have to work together to build castles, roads, fields and abbeys, however there's also competition to build your own structures. In Carcassonne this balance between co-operation and competition is an accurate reflection of life.
Dungeons and Dragons and other role-playing games are also co-operative, where one player (the Games Master, or Dungeon Master) creates the world, monsters, allies, objects, treasure, scenario, etc. or uses a vast range of pre-made books to create these and the players then each choose a character and are responsible for that character's actions only, with dice (often 20 sided) thrown to determine the outcome of fights, spells and other events.
Role-playing allows players to work together, use their imaginations creatively, work out riddles and solve the overall adventure.
Crossword puzzles (like those linked to on the left) are a good way of keeping the brain active and studies have shown that if you do crosswords or other word games on a regular basis, you're more likely to not get Alzheimers or other similar illnesses. Crosswords or other knowledge games such as Trivial Pursuit are also a good way to acquire general knowledge in a fun and relaxed way.