For me it’s my first experience with a 16 bit game console - the Sega Genesis (if I am not wrong). Played Final Fight at my friends place and I still cannot rate any gaming experience higher than that. I have since tried playing Final Fight again, but it’s not the same.
I spent so much time on this topic. And there are some 'firsts' that don't hold up to the magic they had. But some, even though they don't shine as much, still have surprising balance/depth/quality.
For instance, Resident Evil games, have a mood that is unparalleled (I'm exagerating a bit but you get the idea). It's blocky, slow, ridiculous technically for any next gen standards.. but the mood is so on point it makes the game worth it.