Beer is normally made from all kosher ingredients: Water, barley, yeast, and hops. Isinglass finning (made from ground tropical fish), gelatin, and other ingredients are sometimes added to remove dark particles from the beer. Caramel color is sometimes added for coloring. In all, United States law allows over fifty-nine chemicals or additives to be used in beer.
Gelatin and isinglass clarifiers are not used in domestic beer in the United States. Isinglass finnings have been used as a beer clarifier in the UK for centuries. Over two hundred years ago the great Halachic authority Rabbi Yechezkel Landau in his work Nodah B’Yehudah permitted isinglass clarifier (Yorah Deah, Siman 26). A clarifier only filters unwanted particles and is not present in the final beverage.
Fruit flavorings and spices are used to make flavored beers. By U.S. law, these beers must be labeled “Flavored Beer.” Flavored beer definitely requires kosher certification.
“Barley wine” is a specialty beer which definitely needs kosher certification, because it is sometimes fermented with non-kosher wine or champagne yeast.
Obviously, the kashrut status of a product changes with changes in production methods or kashrut supervision.