Fight in the nude was a popular self-imposed challenge for the original Diablo, although it can be attempted in other games in the series as well. It involves completing the game without wearing any items. As an easier variant, one may try to beat the game without any armor, but can use weapons and jewelry.
In Diablo III, there is a series of achievements referring to this one: these achievements are earned by killing bosses without any items equipped on the character (all damage is done by followers). The most famous of these is Naked Lust, awarded for killing Cydaea without any gear. These achievements can prove difficult, however; one mistake can throw the battle in the boss's favor, even with a lot of Paragon levels. Typically, a character will use a crowd-controlling build, with all skills aimed at keeping the boss stunned, slowed etc.
The main difficulty, however, is not even the damage itself: due to the game's mechanics, a follower can only do steady damage while the character is immobile, and standing still even for a few moments may be extremely dangerous, as without equipment, not only is a hero's Life very low, but his/her degree of protection is virtually nonexistent. Some classes have skills (such as Serenity) to make them briefly immune to damage, though.