I've been a big fan of Fighting games ever since I found an old Neo Geo arcade machine at a hotel in Montreal, with KOF '94 being the game I spent about $3 worth of quarters on. (I never did beat the Girls Team) Since then, I've gotten into Street Fighter, Guilty Gear, Marvel Vs., Darkstalkers, Fatal Fury, Blazblue, Tekken, DOA, Soul Calibur, and even more obscure ones, like Rival Schools & Rage of the Dragon, Matrimelee, and some newer ones like Under Night In-Birth.
Actually, I was thinking about it earlier, and I seem to have a hard time thinking of games I've tried that I didn't enjoy to some extent. I know I had trouble getting into Arcana Hearts 3 (I thought it felt really floaty compared to the first Arcana Hearts game), but I still enjoyed it once I got used to it. Marvel Vs Capcom 1 & 2 also aren't that fun for me, they're too unbalanced & Chaotic for my tastes. Same with Melty Blood: Act Cadenza, as well as party fighters like Super Smash Bros. I can still enjoy a few rounds here & there, though, so long as I'm in the right mood.
Granted, I never try to get good at any of them, I mostly just try to see how far I can get in Arcade Mode on multiple difficulties and with multiple characters. Which totally works for a guy like me, who never takes anything seriously. They're the perfect "pick up & play" games, which offsets long RPGs & action/adventure games, which have so many things to keep up with, it can become a little overwhelming at times.
...Well, I guess I've never gotten into any Western Fighting game, now that I think about it. But I mostly figure that's because the ones I've played are blatantly awful, like the early Mortal Kombat games, and Skullgirls.