It probably started with the Intellivision, which my family got for Christmas in 1982. It certainly wasn't much of a system for adventure/RPG games, although there were a few that were definitely inspired by that tradition (two licensed AD&D games, Swords & Serpents).
The first computer-based adventure/RPG that I played was probably The Hobbit on an Apple IIe at elementary school.
My cousin gave me his old Commodore 64 in 1989, when I was 15 years old. That was my first home computer; before then the only computers that I had any regular access to were the handful Apple IIe and Commodore 64/128 computers at school. I'd had an 8-bit NES since sometime in 1988.
The first RPG that I got into on my C64 was The Bard's Tale III. I'd been playing pencil & paper D&D since late 1986, and I'd played the first two Legend of Zelda games on the NES, as well as Dragon Warrior (Quest), Rygar, and a few other games in that general style.
I discovered Wasteland sometime in 1989, and it became one of my favourite games on the C-64. Played a lot of Pool of Radiance as well, and I had copies of Ultima II and IV, but they never really captured my interest (Ultima VI on the PC was the first Ultima that I was actually able to get into). There were a lot of amazing things about Wasteland at that time, notably the relative open-endedness and the non-traditional setting. When I got rid of the C-64 a couple of years later and moved on to my family's 286 PC, I made sure that I bought a PC version of Wasteland.
I had been anxiously awaiting a sequel to Wasteland for a long time (and tried to find out as much about "Mean Time" as I could). I got Fountain of Dreams for Christmas the year it came out, having just read Scorpia's scathing review of it a couple of days earlier. So I didn't open it and exchanged it for something else.
When I first found out about GURPS Fallout and how it was a "spiritual sequel" to Wasteland, I was rather excited and read up on everything that I could find about it (not as accessible in those days, that's for sure). I was only minorly disappointed when they dropped the GURPS license and went with their own system -- and that probably worked out for the best anyway, to have a system tailor-made for the game.
I bought Fallout as soon as it was released and finished it within a week (about 20-22 hours of gameplay time, I think). Played through it a couple of more times by the time Fallout 2 came out, which I of course bought immediately.
I did buy Fallout Tactics from a bargain bin a while after it came out but never played it. Didn't buy Brotherhood of Steel on the consoles, although its existence doesn't offend me in the slightest.
Fallout and Ultima have been my two most highly-regarded RPG series for a very long time now.