There really weren't all that many first person shooters before Doom came along. The hardware of the time just wasn't up to it. Wolfenstein is the most well known predecessor and it came not long before.

I'm not really a huge fan of FPS games and have only played and liked a very few. The thing that made Doom a real standout for me at the time wasn't that it was an FPS necessarily, it was the ability to have a death match vs. other players and the ability to add new player created levels. I don't know that I ever finished the single player game but I probably spent more hours playing Doom (and Doom II) against other people that I've ever spent with any other game. It was the perfect game for my then brand new 486 DX2-66 that I bough right before going to college...