Everquest's designers have credited MUDs as the primary inspiration, I believe. I wish I had a reference, but they one of the creators of a big MUD (Diku I think) was considering litigation at the time :)
I think MUDs are sort of the genesis of most multiplayer online games, but there is some seed in BBS Doors as well (Legend of the Red Dragon etc...) that had some multi-player persistence.
Besides that, obviously pen and paper RPGs as well as fantasy adventure games (Kings Quest etc...) played a role in influencing all of these games.
Everything back then was heavily based on MU*s (ie also MUSH, MUSE, MUX, etc), for instance Designer Dragon (aka Raph Koster) came from LegendMud.
For those who were around back then, there is zero question that many design decisions of EQ were chosen as a direct reaction to the state of things in UO and evolving customer tastes. Put simply, the average gamer simply was not (and still is not) ready for the sort of sandbox that UO initially provided, but a Diku on steroids was definitely in the cards.
I think MUDs are sort of the genesis of most multiplayer online games, but there is some seed in BBS Doors as well (Legend of the Red Dragon etc...) that had some multi-player persistence.
Besides that, obviously pen and paper RPGs as well as fantasy adventure games (Kings Quest etc...) played a role in influencing all of these games.