I was introduced to the genre through Street Fighter II and Mortal Kombat II. I lean more on the side of Mortal Kombat. My favorites of those being II, Trilogy, and now IX. Evil Zone is pretty great as well, especially if you like anime with all the little nods they have to it, and a lot of the characters tie together. Still one of my personal favorite fighting games to this day. And of course Soul Blade/Edge and Soul Calibur III.

I like some Tekken, but haven't played a great many of them. Just 1, 2, and Tag Tournament 2. I only played the first and fifth Dead or Alive games. 5 was pretty good.