Ultima III Exodus (1983) - Origin Systems, Commodore 64
Although there had been two Ultima games before it, Ultima III from 1983 stands above the others in importance. It was the first cRPG (computer role playing game) where you led a party of characters in a fully realised fantasy world (Sosaria), and was the first Ultima game to stand wholly on its own merits (not copying pen-and-paper AD&D rules for the mechanics). Basically, all later party-based cRPGs can be said to originate from the success of Ultima III.
The game was played from a top-down view. Trees, mountains and other natural scenery blocked the view, so you never knew if there was a monster hiding deeper in the forest tiles. When you encountered an enemy unit, you were transferred to a separate battle map where you controlled all of your characters to fight the enemies. The main goal was to destroy the final remnant of the evil left on Sosaria after the events of Ultima I and II, namely Exodus.
Although I love the later Ultima IV the most, Ultima III was an eye-opening game for me as it introduced me to the world of pen-and-paper RPGs. Lacking the language skills and Finnish translations of the real RPGs, I turned to the world of Sosaria and made-do with my imagination and the great world that Richard Garriot had fashioned. It (along with real RPGs) is also responsible for my motivation to learn English.
Elite (1984) - David Braben and Ian Bell, Commodore 64
One cannot talk about the great early computer games and not include Elite; the space trading and fighting game. Elite was first released in 1984 by Acornsoft and it became an instant success. Elite was the first complete game taking advantage of the new 3D vector graphics and it is, to this day, one of the few space games featuring open-ended gameplay.
The main idea of the game was to become ”Elite” - which involved hyperspace travel between solar systems, trading between space stations, scooping cargo from destroyed enemy ships (or trader ships, if you decided to practice a little bit of piracy yourself) or fuel from the coronas of stars, and fighting the occasional pirate ship with laser cannons (or waves of pirates if you were brave enough to enter one of the politically unstable systems or carry extremely tempting cargo, like narcotics). Along the way, you could upgrade your ship and perform a series of secret missions, like taking out a stolen top secret military spaceship.
Out of the three games mentioned here, Elite definitely received the most gaming hours from me and continued to do so on various platforms and incarnations for years to come (check out Oolite, if you are interested). I'm still hopeful that someday we will be treated with the elusive Elite IV.