BoingBoing, there is an interesting article about why beer batter makes fried food delicious at Scientific American. In short, beer contains three things that make it a great batter ingredient: foaming agents, carbonation (a.k.a. dissolved carbon dioxide), and alcohol. Carbon dioxide is more soluble in water at cold temperatures, so when beer batter is heated it releases bubbles of carbon dioxide that are trapped by the foaming agents (in most beers this is carbohydrates and proteins from the barley malt), making a light crispy crust. The pockets of air in the crust insulate the delicate food inside, allowing it to gently steam and keeping it moist. The alcohol in beer batter boils at a lower temperature than water, meaning that, when cooked, this batter releases moisture faster than batter made with just water, allowing it to cook faster. Only after all of the water and alcohol have evaporated will the Maillard reaction* take place, making starches and proteins in the batter golden brown and delicious.
*Note: The article says that the Maillard reaction takes place above 130 degrees Fahrenheit, but this is incorrect. It actually takes place above 130 degrees Celsius, which is about 265 degrees Fahrenheit.
Another good reason to cook with beer, and not necessarily just in beer batter, is that beer adds great flavor to dishes. Beer contains its own flavors - smoky, sweet, bitter, or acidic, or a combination of these, depending on the variety. Beer also contains alcohol, which helps amp up other flavors in a dish. Alcohol is able to dissolve many flavors that are not very soluble in water, like essential oils and other organic compounds. These compounds are key flavor components of foods like black pepper, chili peppers and tomatoes, among many, many others. This means that adding any alcohol-containing liquid to a dish can dissolve these flavor compounds, making them more available to your taste buds and increasing their flavor.
In case all of this had put you in the mood to cook with some beer, I've included a recipe below for Black Bean and Sweet Potato Chili, which I whipped up for the Superbowl last Sunday. It's delicious, cheap, and healthy, and the dark beer included in the recipe adds a little smoky flavor as well as some alcohol to dissolve the spicy and tomato flavors in the chili.