Fur is an item dropped by wargs and bears when they are slain. Wargs can drop 0-2 pieces of their fur upon death, while bears always drop 1-3 pieces. A weapon enchanted with "looting" will result in more fur being dropped.
Although there are four different colours of wargs in Middle-Earth (grey, brown, black, and white), they do not drop differently coloured fur accordingly to their own colour; they all drop the same type, which is shown in the picture on the right.
Fur is primarily used to craft fur armour, which is slightly stronger than leather armour, and just as protective. However, if you're not armoured, hunting wargs or bears for fur to make armour is not recommended – it's often easier, and far less dangerous, to make bronze armour or iron armour.
Despite its weaknesses, fur armour has one important property: it blocks the cold better than any other type of armour. Thus, it is extremely useful to have this armour on hand if one plans to visit Forodwaith. Leather armour also helps block the cold, but not to as great an extent as fur does.
Until Beta 31, fur and the items it is used to craft were entitled warg fur rather than simply fur. This was because, prior to the addition of bears in Beta 31, wargs were the only mob which dropped fur.