Beard and mustaches are an essential accessory to many costumes. Some costumes, like Lincoln or Santa, absolutely require a beard. Others are just greatly improved by facial hair. There are so many styles that you're sure to find the perfect set of whiskers for your costume. Think of all the famous characters with beards and mustaches. Abraham Lincoln is far from the only one. If you want to go Biblical you're going to need a full beard for your Moses or Jesus costume. Pirates like Captain Jack Sparrow and, of course, Blackbeard had lots of facial hair. Even Tony Stark has a mustache and goatee. Pancho Villa, Fu Manchu, and Zorro had mustaches.
Any pirate costume is improved with a big beard. The same is true for cowboys, hippies, and hillbillies. You aren't limited to full beards, though. There are long, thick goatees and huge mustaches. There are even several styles of sideburns, including big lamb chops for your Civil War, biker, or 60s look. There are even beards without mustaches for an Amish style.
Mustaches come in every imaginable style too. Huge pancho or walrus mustaches that cover the mouth are perfect for a cowboy, Mexican, or hippie costume. Small, dapper, curved mustaches suit a proper Victorian Englishman or a steampunk outfit. Thick but trimmed mustaches are great for cop costumes and 70s swingers.
Beard and mustache accessories come in a huge variety of styles. Some packs even contain several mustache styles. Some of the facial hair is held on by a nose clip or elastic band, some are self adhesive, and the more professional ones require spirit gum. If you need facial hair for your costume and can't grow your own, an accessory is the way to go.