Fighting games were my thing but I was never in the competitive spirit so I stray from playing with others who are. Anyway, my personal favorite fighting games are Smash Bros and MvC2. Other type of fighting games I love are beat 'em ups, especially Final Fight and Streets of Rage. I just downloaded Streets of Rage Remake v5.2 recently and I love the new unlock system they have. It's worth playing the game the normal way for because the unlockables in SORR are worth replaying the game over and over again even though it has 4 routes (SOR1 Route, SOR2 Route, 2 others with SOR3 stuff in it).
My other favorite genre of gaming is SHMUPS. Yes, arcade styled shmups but the only shmup I play is the Raiden series, especially 3 and 4 since I own Raiden 3 for the PS2. I might get Raiden 5 for my Switch some day.
Beware the Dark Wolf once more!