The other day Mom picked a tomato off one of her several plants. It was smiling brightly red at her, so she assumed it was ready to go. Well, the back quarter of the tomato that she couldn't see while the tomato was still on the vine was fairly green. What to do?
Put the partially-ripe tomato in a bag with an apple or two and set it out at room temperature for a day or several (you'll want to check on it) and it will ripen for you. Basically, this is the same trick that the big growers and supermarkets do with a fair amount of their produce, only they don't use the apple directly.
Apples put out a gas called ethylene gas that causes many fruits (e.g., peaches, pears, bananas, apples) to ripen. The growers pick the produce green (so that it will ship with less damage because the green fruit is very solid) and the markets (or middle-man) then gas the fruit with ethylene gas for a while before putting it out on the shelves.
You can use this tip at the end of the growing season when your tomato vines are still covered with partially ripe or unripe tomatoes and extend your tomato-eating season. (Of course, there's always fried green tomatoes, if you can handle the oil.)
The bad news is that the tomato doesn't really continue to develop its sugar content much once the fruit is picked, so tomatoes (and most other fruits) ripened this way tend to taste a little more flat than those picked when fully ripe. (This is one of the reasons that supermarket fruits don't taste as sparkly as the home-grown versions.)
Oh, and that saying about one rotten apple spoiling the barrel? Well, it's true. An overripe/rotten tomato REALLY puts out a LOT of ethylene gas and sends the rest of the barrel into an over-ripening frenzy.