This is a fun thread. Always fun to see what fighting game fans are enjoying. For me, there are too many great brawlers to choose, especially on my beloved Sega Saturn.
Street Fighter 3: Third Strike - Loved this game on the Dreamcast, and I've always gone back and forth between Third Strike and Alpha 3 as my all-time favorite Street Fighter. For now, I'll choose the newer title, thanks to its wonderfully fluid animation, great character roster and back-to-basics gameplay. Also, the music absolutely kicks.
Fighters Megamix - Normally, I'd say Virtua Fighter 2 is the best fighting game on Saturn, certainly the one that shocked and dazzled the most when it was new. That said, the game is extremely unbalanced (there is a definite pecking order), and the expanded moves and techniques in VF3/Megamix is much more entertaining. This game is just pure unadulterated fun. Yes, half the characters are "joke characters." So what? The gameplay flows like greased lightning, is endlessly exciting and immensely deep. And I get to beat up the Daytona car.
Asuka 120% Burning Fest. LTD. - For my third entry, I'm choosing a title that has never achieved more than cult status, but is nonetheless one of the true classics of the Japanese Saturn library. Gameplay is extremely swift and intense, combos and strategies are fairly easy to learn, and matches can quickly elevate (or devolve) into sensational 20-hit combo smackdowns. I also really enjoy the graphics, which are bright and colorful, and feature solid animation in its fighters. There's no animation whatsoever in the backgrounds, but what do you expect from a videogame made by only two guys? Seriously, check Asuka out by any means necessary.
