I can't pick since there are many series that I love.
In no particular order; Tekken, Blazblue, Mortal Kombat, Persona 4 Arena, Dead or Alive, Super Smash Bros, Marvel VS Capcom, Dissidia, Bleach DS fighting games and Arcana Heart are some of my favorite series.
I would buy a next gen console, but Warriors Orochi 3 Ultimate (Despite having Sophitia and Kasumi pre-installed on there), Wolfenstein New Order, Infamous Second Son and Sniper Elite 3 aren't enough to make me buy a PS4 or Xbox One.
All of the above. Plus Guilty Gear, Marvel vs Capcom, Blazblue, Virtua Fighter, Smash bros, Godzilla Destroy all monsters Melee, King of Fighters, Fatal Fury, Skullgirls, Snk vs Capcom, Megaman: Power Battles, King of Monsters, Injustice (minus having superman in it), Kick Beat, TMNT Smash Up, Godzilla Unleashed, Dragonball Z fighting games, Bleach fighting games... I love the fighting game genre.