First, let me explain that my parents were gamers, which explains why I'm such a gamer. So, it was only natural that my dad had Doom for our Super NES--though I'm not sure which version he had, I do remember that the game cartridge was red. Just the thought of it makes me cringe.
I absolutely HATED this game when I was little. But you hafta remember that when it came out, I was only 3 years old and still believed in monsters and all that business. This game horrified me. Now that I'm a little older, I have a greater appreciate for the game. In fact, if I took the time to play the game on my old Super NES (if I still have the game, which I don't think I do for obvious reasons), I bet I'd actually enjoy it, despite the crappy graphics, mostly because I can see how far we've come from Doom. In a way, it was the archetype for Halo and other first-person shooters. But, I also have to say that given the choice, I'd pick Halo over Doom, not even because of the graphics, but because it actually has a story line that I can enjoy.
It was fun to run around in Doom for a little while though!

I thought it was interesting that you brought up age, because I think that is a huge factor. Like you said, at such a young age you could not appreciate a game like Doom, but now after experiencing several other games you can enjoy playing it. I think a lot of the games that we might not have liked when we were younger would be really fun for us now!
It wasn't until Halo that I actually enjoyed 1st-Person shooters. When I was younger (not as young as with Doom), I tried the N64's James Bond: Golden Eye, but I confess that the only way I'd play it was with a Gameshark that enabled cheats such as paintball mode, invincibility, and invisibility--sometimes all three together. I'd sit and watch my cousin play Golden Eye to unlock new levels, but the whole idea of people shooting me scared the crap out of me.