Because the flavors in wine are stronger when cooked, it is important to select a wine whose flavor you like, and you think would complement the other ingredients in a recipe. There is a reason why dessert wines such as Sherry and Sauternes are used in dessert recipes: they're sweet.
Avoid wines labeled “Cooking Wine” that you find in supermarkets; they are typically salty and often have other additives such as food coloring. A rule of thumb is to only use wine that you would drink on its own. If you don't like the way it tastes in the glass, you probably won't like it all over your food, either.
The best all-around wine when a recipe calls for "dry white wine" is a Sauvignon Blanc. The grassy, herbal flavor will complement just about any dish.
For long-simmered meat dishes calling for a dry red wine, try something hearty, like a Zinfandel. Or if the dish is lighter, you might want something lighter like a Chianti.
There is a place for fortified wines in the kitchen as well. Port, Madeira, Sherry, and Marsala all lend a richness and sweetness that are harder to get from other wines. Marsala works both in desserts and in sautés, such as sautéed mushrooms. Port is another good choice for heavier meat dishes, like casseroles.
Wine is also great for deglazing a pan. Deglazing is the process by which you make a sauce with the cooked bits left behind after food, often meat, is cooked in a pan. Once the food is removed and the excess fat is poured off, add the wine and heat, scraping with a spatula to loosen the browned bits. Depending on the quantity and flavor needed, more wine, butter and/or herbs can be added.