I haven't played current gen fighting games, but pre-2005 stuff I played them quite a bit because my cousin is a fighting game fan. I used to play Street Fighter, Mortal Kombat, Killer Instinct, Tekken, Dead Or Alive mostly. I did play Virtua and Soul Calibur, but only once or twice, so I'm not all that familiar with the mechanics and characters of those games.
Mortal Kombat 3 was pretty much my introduction to the genre, and I was a fan of all the colourful characters in it and the mythology surrounding it. I checked out the previous installments of the game, but at the time I felt MK3 was still my favourite because of how much more elaborate it was compared to 1 and 2. Hey, you grow up with a sequel, you get spoiled.
Killer Instinct pretty much was next in line. Right now, I feel as though it copies Mortal Kombat in a lot of ways, but at the time I didn't see it because I hadn't played all that many games. It had an interesting combo system and a great soundtrack.
I was introduced to Street Fighter relatively late. It was SF2, of course. It didn't stick all that much with me. until I played a Street Fighter EX game from Arika on the PSX. I know a lot of people deride the SF EX series, but I have fond memories of them. I'm a fan of the characters Pullum Purna, Garuda, and D. Dark.
It was SF EX 3 that was among the games that introduced me to the next generation of consoles, among others the PS2 which my cousin owned. Aside from SF EX 3, I also played the better-known games Tekken Tag Tournament and Dead Or Alive 2. I played the heck out of both games, though between them, I'm partial to DOA 2, simply because the gameplay seems to be more fluent. I was blind to the cheesecake in DOA, and Kasumi remains one of my all-time favourite fighting game characters next to SF's Chun-Li.
That's about it. I also played Super Smash BRos. and SSB Melee, but not Brawl. I think it was an interesting take on the fighting game genre, with a different, original fighting system.
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clarity of thought before rashness of action