Monopoly would be a good one if there was a quick play version---say first to achieve a reasonable dollar amount; not really high in strategy in my book, but seems to be a childhood favorite with a lot of people.
I'd see about a quickplay version of Risk too (e.g. make a custom map with less territories on the board, or limit the number of times replacements are received).
Good god, why would you punish children by making them play such a poorly-designed game? Monopoly is a game that is saturated in money, and the only way the game ends is if money is removed from the game (or is entirely transferred to one player). Add to that all the little "kid" rules like the Free Parking money fountain and you've got a seriously flawed game.
Settlers of Catan maybe?
Risk II is a good one, with adjustable rules/settings. Same time Risk is pretty neat.
Chinese Checkers
Chess is very good at any age. Checkers for the people who don't get Chess. Go and Pente are interesting games if someone can teach it. Stratego is pretty fun for kids too (not sure of the game length). Reversi and Connect-4 were fun when I was young. I also played a bit of Mastermind as a kid. Related would be Battleship.
Cataan is a fun game, but it definitely runs at least an hour when I play it.
Chess is a solid one, the classic game of balancing long-term strategy and short-term tactics, and the three dimensions of material, space, and time. I highly recommend it.
If you are interested in board games rather than computer games, then I'd suggest:
Settlers of Catan (+ expansions)
Agricola (+ expansions)
Puerto Rico
For a bit older kids:
Caylus
Le Havre
Now we are talking. Agricola and Puerto Rico are pretty solid games but there is a learning curve associated with them. I'd recommend starting with the gateway triumvirate: Settlers of Catan, Dominion, and Ticket to Ride. Each game is fairly simple to learn, relatively fast, forces you to plan ahead and manage your resources wisely, and is a combination of competitive and cooperative elements (well, weakly cooperative in Dominion based on cards, and in Ticket if you use the stations from the Europe board).
I add to the list St. Petersburg. It's a pretty simple and fun game where you start off with a certain amount of money, and you buy cards to generate more money and points. Guy with the most points wins. It doesn't get a lot of attention, but I would stick it in the list of great entry games. It's long been a favorite of mine.
Later on, Power Grid. It is the Game of the Gods Themselves. You compete in auctions for power plants, buy fuel, and place stations on a map of any number of different countries to build the largest and most profitable electricity company. It is amazing and can typically be played in 2 to 3 hours. Several different map expansions give you different tweaks and keeps the game fresh.
In general, I don't recommend computer games for kids, at least not RTS. If you are looking to teach strategy, you have to give them time to think and consider moves, etc. The reflex-oriented unit micromanagement in RTS games is not the same thing. Furthermore, if you plan on saving a TBS and playing it over multiple days, you are implicitly expecting the kids to remember their thought process, strategy, and details without getting bored over the same time period. For elementary school kids, that might be a stretch. That's why I like the gateways: Dominion (30 min), TTR (1.5 hours), Catan (1.5 hours), and St. Petersburg (1 hour)--all can typically be played within a single gaming session, and are fast-paced enough that kids won't lose interest like in Monopoly or Risk (especially when someone else is on the warpath and you aren't doing anything but watching them roll dice and move armies).
read over that the question was for computer games.
