The list of games I play or have played is too expansive, so I'll just do a brief history of the games that meant a lot to me in my lifetime.
My brother and I owned an SNES when I was growing up, so we played a lot of fighting games on it. Out of all of them, we probably played Killer Instinct and Ultimate Mortal Kombat 3 the most. When he got a Playstation, we continued the trend. He had a friend who was more into fighting games than either of us, and he brought a bunch of stuff over that the three of us played. Street Fighter Alpha 2, Darkstalkers 3, Marvel Super Heroes, Tekken 3. Around this time I was old enough to go to an arcade, and while I didn't have a scene at the local arcade, I played through the single player of Marvel vs Capcom quite a few times.
When BlazBlue CS1 came out, that was the first fighting game I got into competitively. I started going to tournaments for it, and while I wasn't very good, I was having fun just playing other people. When Marvel vs Capcom 3 came out, that was the first game I really dug deep into and got pretty respectable at. During this time I dabbled with a bunch of games, but MvC3 and it's sequel were and continue to be my main competitive fighting game.
However, it's not the only game I've entered tournaments for. To date, I've entered tournaments for Ultimate Marvel vs Capcom 3, BlazBlue (whatever the most recent version at the time is), Skullgirls, Vampire Savior (Darkstalkers 3), Street Fighter III: Third Strike, Street Fighter x Tekken, Persona 4 Arena, Mortal Kombat X, and Guilty Gear Xrd. I've already pre-ordered Street Fighter V, and like what I've played so far, so I can see myself entering tournaments for that game as well.