When I was a kid, I felt pretty confident no video game would ever top Dragon Quest 4 (known as Dragon Warrior 4 to me, at the time).
It has been since surpassed, but I do still think it's pretty damn excellent.
Other big games for me were Ultima Online, later World of Warcraft.
Prior to those MMOs though, I was a big MUD (multi-user dungeon) player. I used to connect to Arythia.org via zMUD or old telnet and spend hours at a time playing and chatting with people in the entirely text-based proto-MMO
Edit: typos and a clarification added