Their exact description varies by region - in Sweden and Denmark they are usually reanimated corpses in or near their burial mounds, guarding the treasures they were buried with, and often with an insatiable appetite, somewhat like the George Romero style zombies, they would usually bit or eat their victims, who would then rise as a Draug themselves. In Norway they are often the bodies of drowned sailors, they would appear swimming alongside ships sailing near where they drowned, or near the shores, and they would appear as humans, but with their head replaced with seaweed, or being entirely headless.
Unlike zombies they retain some or most of their intelligence in death, and often possess the ability to shape-shift or increase their size and weight. In some stories they can enter dreams and drive their victims mad. They may also appear as a cat, laying on their victims chest when they sleep, and then grow until the victim suffocates.
In The Elder Scrolls games, primarily in the Morrowind expansion Bloodmoon and in Skyrim, the mound dwelling Draugr are common enemies. The aquatic kind also appears as Dreugh in Morrowind and Oblivion.
In The Witcher 2 the Draug is a massive boss encounter with the ability to shape-shift and summon Draugir soldiers.
In The Secret World the Draug appear as swollen humanoid creatures, with seaweed growing on them and with crab-like claws, rising from the seas and attacking coastal towns.