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Although an argument could be made that Lucasfilm's 'Habitat' (beta release 1986) is the true answer to this question, being the first attempt at establishing a large-scale virtual community with graphical avatars etc., that title was more of a virtual chat environment than a conventional MMORPG as we know them today. Instead, Neverwinter Nights is more commonly recognized as being the first multiplayer online role-playing game to be based on graphics.
Developed collaboratively by Stormfront Studios, AOL, Strategic Simulations and D&D publisher TSR, Neverwinter Nights was released on AOL in 1991. The game initially cost $6 an hour to play and its servers supported 50 players but it was eventually bundled into AOL's subscription cost and saw peak activity levels of 115,000 players around 1997 when it was closed down (at least partially due to pressure from Ultima Online, which launched the same year). EverQuest and Asheron's Call didn't arrive until 1999.