Contrary to popular misconception, adult badgers do not have any natural predators in Britain or across much of Europe. Larger carnivores, such as wolves, lynx and bears may sometimes kill badgers, but this appears to be to remove potential competition for food (i.e. competitive displacement), rather than predation (i.e. with the aim of eating them). Nonetheless, in his book Badger, Tim Roper notes that badger remains have been found in the droppings of wolves (Canis lupus) in China, Finland and Italy.
Roper also mentions that radio-collared Eurasian lynx (Lynx lynx) have been observed attacking badgers in Switzerland, but doesn't provide any further details. Overall, however, badgers do not appear to be a significant prey item of lynx. Between March 1988 and May 1998, for example, a team of biologists from the University of Bern, led by Anja Jobin, examined 617 kills made by 29 lynx radio-tracked in the Jura Mountains on the Switzerland's north-western border with France. One of these kills was a badger, representing 0.2% of the prey items these lynx took, although they authors don't say how common badgers were on the study site.
Cubs are slightly more vulnerable and, in the UK, they may fall prey to golden eagles (Aquila chrysaetos), buzzards (Buteo buteo) and red foxes (Vulpes vulpes). In Europe wolves, lynx, wolverines (Gulo gulo), brown bears (Ursus arctos) and eagle owls (Bubo bubo) are potential predators of cubs and juvenile badgers. I'm also aware of at least one confirmed case of a badger cub having been killed by a domestic dog in the New Forest in Hampshire.