I am playing this very cute little game now called Virtual Villagers. It is played in real time and can run even when the computer is off. It does run a bit slowly but it is a welcome change from faster games like Neverwinter Nights and Diablo.
You have this band of little people who become shipwrecked on a tiny island and you have to help them to survive. There are 16 puzzles on the island that you have to figure out while keeping your villagers alive.

The villagers can learn different skills like Farming, Science, Breeding, Healing and Building, all of which are necessary for the village to survive. The first few times I played the game I did not know that you could put the game on pause while you left for a long period of time so I would wake up many mornings to find many of my villagers dead. Now that I have found this great tool I am playing the game on the hard level to see what will happen.

In addition to going about their daily lives the villagers have to deal with a few mystery island events. These are random events generated by the game and they add quite a bit of variety to the lives of the villagers. I just experienced one event where a curious monkey mixed up some ingredients on the research table and gave the villagers technology points.

The scientists in the group do research at a table and earn research points. These points can then be used to purchase skill levels for the villagers. The first level of farming that the villagers can purchase allows them to plant their own food instead of living off berries from a bush. When they earn enough points to purchase the next level of farming the villagers can purchase the fishing skill which allows them to catch fish to supplement the berries and the vegetables.

This game is VERY addictive and I have it running every time my computer is on. I periodically check my villagers to see how they are doing but the game basically runs on its own with very little input from you once you get started.