If you've been reading these posts, you know that I started playing D&D with the Moldvay Basic set. Thus, it should come as no surprise that the first dungeon I explored was the Caves of Chaos from Keep on the Borderlands. My friend Dan was the DM. I played my fighter character, Serafis. It was a great introduction to dungeon crawling. Years later, I played it again modified for AD&D in college. It was still a lot of fun.
The first dungeon I ran as a DM was a home brewed adventure I came up with for my high school group. I can remember that I called it Morblund Castle. The basic premise was that there was an old castle that had been taken over by an evil wizard. (Really are there any other kind?) He hadn't been seen in over twenty years and was assumed dead. The party was hired by the king to check out the castle with an eye to renovating it and to remove any dangerous items left by the wizard and clear out any monsters that might have moved in. Needless to say, there were plenty of both.