It just makes sense to cook with beer. Beer has more in common with a lot of the food that we eat than does that other popular cooking beverage. It contains grain (barley), herbs (hops), water and yeast. Wine contains grapes. Adding beer to a recipe can really change the character of the dish. It can enhance particular ingredients, help blend the flavors of the dish, or just add that little zing that your meal might be lacking.
Don't be afraid to experiment when cooking with beer. Naturally we've all heard of beer batter and the recent grilling phenomenon, the beer can chicken, but you really need to try to think outside of that box. A nice start is with a loaf of beer bread. Most cookbooks have a recipe for one but it's really not necessary. Just replace some or all of the liquid in a bread recipe with beer. Or try other things such as deglazing with beer, a sort of of coq au beer, add beer to stew … you get the picture.
There are a few things to remember when experimenting with beer. As with any other liquid, when you cook with beer you will almost always reduce some or most of the liquid away which will magnify its flavors. For instance, if I were to make a brown gravy using beer instead of broth or water I would opt for something like a sweet stout with little hops bittering because I don't want bitter gravy.
Another point is that, as any homebrewer can tell you, the delicate aromas of your favorite beer will be lost if you boil it for very long. Many beers are prized for the hops in the nose. This aroma results from the oils of the hops cone which quickly dissipate when boiled. So if you're going for that hops aroma in, say a soup, try a splash of your favorite IPA after reducing the heat. If you're going for the deep rich flavors of a darker beer in a stew, add it at the beginning and boil it with the rest of the ingredients that you normally would. The mellow sweet and roasted flavors of the barley will stay with the stew and blend with the flavors of the other ingredients.
Never cook with a beer that you wouldn't drink. If it doesn't appeal to you as a beverage, chances are it wouldn't appeal to you in a recipe.
The most important point is to experiment, experiment, experiment. Virtually any recipe that calls for a liquid of any sort could be replaced with beer. Think it through, though. A Berliner Weise probably wouldn't work for that bread recipe I mentioned earlier but it might be just the thing to brighten up a stir fry.
You can start with some of the recipes that I've linked to in the Cooking with Beer category. If you have a favorite recipe that I haven't linked here, I'd love to see it. Send it in and I'll add it to the list.