I originally played it because it was the sequel to a very favorite game of mine (the original LoZ). Back *Then.*
Nowadays, when I play it... besides the "challenge" cliche', it's for nostalgia. I play it for the same reason that I'll fire up a game of Centipede or Adventure on that Atari 2600 PS2 emulation I've got, or why I sought out an online emulation of The Oregon Trail to play (before I caught a virus from the site I found it on...grr). Pure. Frigging. Nostalgia. (I'm old, you see).
Also, I actually do like the designs on some of the enemies - floating eyeballs, fire-spitting gryphons and bird-headed knights are just fun to look at for me. I like the overworld, too. Yeah, it's boring that the townspeople all look the same (but you have to remember the lack of graphics capabilities back then), but the overworld in AoL is vast and has many different towns. I actually find it refreshing to go back to the game after playing some of the modern titles because the modern titles have few population centers, making Hyrule sort of a ghost-town kingdom. AoL shows a world thriving enough to have loads of settlements, like a proper kingdom.
I enjoy going back to a game that doesn't hold your hand. LoZ, AoL and ALTTP are all games where you didn't have a Navi or a Fi holding your hand as you went - you had to figure out things on your own.
And, finally, Error is awesome.