Originally Posted by The Complete Encyclopedia of Vegetables and Vegetarian Cooking
Eggplants should feel heavy and firm to the touch, with glossy, unblemished skins. They will keep well in the salad drawer of the fridge for up to two weeks.
Alton Brown of Good Eats also says it's a good idea to choose a male eggplant over a female eggplant if you can, I think because females are seedier. If you have the opportunity to watch that episode, he shows you how to tell the difference, but I was never able to apply it at the store.
Most sources also recommend salting the eggplant before using it to draw out extra moisture and bitterness.
There are lots of different recommendations for different vegetables. That's where a vegetable book comes in handy. But most vegetables do best if kept in an environment that's not too dry, but not closely wrapped enough to allow condensation to form. Loose plastic wrap or a plastic produce bag left open works well.
Off the top of my head, tomatoes are best kept at room temperature and usually they're better if you let them ripen a few days before you use them.
Cucumbers will keep a long time if they are the precisely correct temperature (I think it's just lightly warmer than most refrigerators, like 42 F or csomething) but otherwise, they tend to go bad very quickly.
Greens are best washed, dried very well, and loosely wrapped or placed in a plastic carton that's not quite airtight.
Onions, potatoes, and other root vegetables do best in a drier environment than other veggies. They also don't need to be kept as cold. Ideally, they'd be in a root cellar, but who has a root cellar these days? The ever-trustworthy Alton Brown suggests keeping them in a bin of sterilized dirt in the fridge, if you have room.