Many other fantasy works have used trolls in the "large, strong and stupid" role of D&D ogres, with the stone-based giants of Pratchett's Discworld and the grey-skinned mountain trolls of Harry Potter being particularly original or well-known examples. The troll of D&D, however, has no real resemblance to these, or to the mythic creature; Gygax instead stated that his inspiration was the 1961 novel Three Hearts and Three Lions by Poul Anderson, which features a regenerating troll, along with a number of other tropes he adopted for the game.
1E
Trolls are initially shown as cadaverous humanoids with a green or grey warty skin, exaggerated facial features, including a long pointed nose, and writhing tendrils in place of hair. The eyes are large black wells beneath a pronounced brow ridge. Trolls possess no visible genitalia, and so presumably do not reproduce in the human fashion, and have only four digits on their hands and feet - even then one of the toes appears vestigial.
Physically, they are powerful creatures, able to deliver a rapid series of blows, each more powerful than a typical sword-strike, and they have a rubbery hide that's thicker and more resilient than rhino-skin. Even without their regenerative powers, they are about halfway between ogres and the smallest of true giants in their ability to soak up damage - although some of this could be due to simple combat prowess, or a lack of truly vital organs. They also have acute senses, particularly smell (which would explain the large nose).