Determining whether or not your beer is vegan-friendly can be difficult; here are some guidelines to help to identify this a little easier.
Veganism, in the strictest sense, allows no products or byproducts that are of animal origin.
Now, adjuncts produce some pretty obvious non-vegan beers. Honey beers, for example, are brewed with honey and are naturally excluded. It isn't always that obvious, though. Sometimes beers will be named after things that they are associated with but do not include. Cream and oyster can appear right there on the label and yet no cow labor or oyster fatalities were involved in the brewing of that particular beer. On the other hand, there are many examples of milk and oyster stouts that do include these ingredients so it's up to you to investigate.
Fortunately, the good beer movement makes your investigation as easy as turning the bottle over and reading the label in many cases. Smart brewers know that they are dealing with a more specialized market these days and want to provide as much information as they can to the customer standing in the beer store.
Things aren't quite so clear on the finings side. Traditional finings, which is used to clarify beer, include gelatin and isinglass. Since both of these are animal byproducts the resulting beer is not vegan-friendly. Fortunately for beer-loving vegans, these are mostly used by the very traditional brewers. Modern filtration equipment makes the use of less efficient but easier to store adjuncts possible with equal or even better results. In my experience, most of the today's brewers use the later method of fining and filtration.
The investigation on this end of the vegan beer question isn't quite so easy. Since finings falls out of beer and doesn't make it into the final product, they aren't considered ingredients in the traditional sense, but, by vegan standards, they are.
There is a website, barnivore.com, which tries to keep up with which breweries brew vegan-friendly beer. The brewing community is so fluid, though, that this seems to be a nearly impossible task. While in most cases you can probably rely on carnivore's list, the only way to be absolutely sure is to call the brewery and ask.