For beef stews, we really like using porters. These beers tend to have a lot of caramelized and toasted malt flavors that work very well with slow-cooked meat, but without going into the coffee-like bitterness of many stouts. Recently, we've really enjoyed cooking (and drinking) the Edmund Fitzgerald Porter from Great Lakes Brewing and the Black Butte Porter from Deschutes Brewery.
German doppelbocks and German-style double bocks would also be an interesting choice for beef stews. They tend to have robust nutty and bread-like flavors with less emphasis on the hops.
When we're making a vegetable soup like minestrone or mushroom-barley stew, we usually go a little lighter. We might still use a porter, but less of it. Brown ales also give veggie stews a nice layer of savory-sweetness, though we'd avoid the "nut brown" ales as they are often too sweet and syrupy for these purposes. Try Brooklyn Brewery's brown ale or the Saranac brown ale.
For all stews, we'll use a half a cup of beer to deglaze the pan and then add another half a cup along with the broth. If we decide we want a little more of the beer flavor after the soup has been simmering for a while, we add more a half cup at a time until it's just where we want it.
What styles or specific kinds of beer do you like in winter soups and stews?