I am disturbed by the number of people citing Ultima: Exodus and Ultima: Quest of the Avatar as games that "made them a gamer" (okay, the number's only two so far, but that's two too many by my count, made worse by the fact that they're both within the first ten or so posts). Those two games completely turned me off of RPGs for the longest time. No clues given as what to do, encounters that scaled by level and made it undesirable to level up. First-person dungeons -- I've never liked first-person, and this was far from its best implementation -- which almost required map-making, which I sucked at since I was like ten years old. A terrible interface in almost every form, and the one time in Exodus I actually found some sort of fire-forge thing in a dungeon that seemed like it might actually threaten some sort of progress, I branded one of my characters with it and he promptly died as a result, leaving me dead in the dungeon with no progress to show for it. I never did find that fire-alter, again, either.
If it weren't for two games which convinced me that RPGs in and of themselves weren't terrible, I probably wouldn't play the genre at all today, which would be a shame since it's probably my favorite. The first game was The Magic of Scherazade, a neat Zelda-like game with the occasional RPG-style battle during screen transitions, and the second was Dragon Warrior III, which had great box art and sounded cool on the back. Only the fact that it was an RPG kept me from trying it for a couple years, and then I only tried it because I had tried most of the other interesting titles in the store and the former game had convinced me that an RPG-style battle system did not suck by its very nature. A friend and I fell in love with the game, and we eventually beat it over the course of about a half-dozen rentals. I've liked RPGs ever since, though I suppose technically it was Final Fantasy II/IV that really started my love affair with the genre.
Technically, though, my first-ever video game experience (outside of maybe a coin-op game at a pizza parlor) was Contra, which the neighbor kids owned and which I borrowed and played the heck out of when I finally got my own NES. I got pretty good at it, too. I could make it to level five on three lives, and level seven on all three continues. No Konami code required.
Actually, I stand corrected. My first ever video game experience was on the TI (Texas Instruments) something-or-other. I just called it the TI, and it had a bunch of cool games. Parsec (a space shoot-em-up) was the best, but Blasto (a tank battle game) and A-maze-ing (a game where you're the mouse and have to run a maze while dodging the cats) were also pretty cool.
If anyone knows what that last system I mentioned was, let me know, will you? I know the Escapist community frowns on emulation, but I really hope someone's preserved a digital copy of those games somewhere. They were too good to consign to the digital garbage heap in the sky.