Definitely Mortal Kombat I always loved Rain and bought the DLC of Rain in Mortal Kombat 9 lol
my friends would be annoyed cause thats all i played as.

Mortal Kombat. It was the first "mature" game I played as a kid, and I still love it to this day. The over the top violence, the characters, the dark humor, everything is just too good in the world of Mortal Kombat.

SonicFan22 : I remember in the old school genesis game of Ultimate Mortal Kombat 3 I think it was that game not sure, but Rain was severely buffed with that ball he had that paralyzed the opponent and you can move him around, if you timed it right you were unbeatable.

taterii : Same here it was my first mature game as well, really it is an iconic game everyone I ask has at least have heard of the title. 

gamerforlifeforever2 : Super Smash Bros. in it's own right became legendary really. It sets its self apart from most if not all other fighters, the only fighter that comes remotely close is the vs series (Capcom and such).  

Soul Caliber 2 was the most memorable game to me in the fighting genre. It is an amazing game that I got for the game cube only about 6 months ago, but it is still pretty amazing to me. But then again, I'm not very big into the fighting genre.

Barathemos : Very good choice, love the Soul Calibur Series, Soul Calibur 2 was a classic, they made the special guest characters famous that series.

I will only summon my most memorable fighting game in only 3 words.... Super Smash Bros.

The reason I picked Super Smash Bros. If you combine a number of Nintendo characters into one single game with a fighting style, I think that just adds the mix of a great game, although sadly, it only come once every video gaming generation, but hey, it is at least worth it though.

IgorBird122 : Awesome answer, imagine if they implemented like almost a full cast of pokemon characters in the next game. And you never know there could be another for the Wii U it's still early. 

Lycan212 : Man, having 719 different Pokemon characters in Super Smash Bros. 5 (unless we go into Generation VII in Pokemon which more likely we will), I think they should have 5 Pokemon characters fighting and have more Pokemon in there like have a Poke Ball have low end Pokemon, an Ultra Ball for high end, non-legendary Pokemon and a Master Ball for Legendary Pokemon. I think that would be really great to see in a Smash Bros game in the future, let's hope they add that in Smash Bros. 5

I also heard rumors that Nintendo has already starting to work on Smash Bros. 5 already.

Mortal Kombat and Street Fighter 2 are the ones that stood out the most to me, I remember they had a Mortal Kombat arcade machine at the 7-11 prior to us having it on home consoles, allot of us played on that, though later we played allot of Street Fighter 2 on SNES at a friends house.

Thinking back on those two games, I did`nt really have a preference and still probably don`t, we all just enjoyed it until we were out of quarters or just tired from playing.  Those would be the two that stand out the most to myself, seeing as I had the most fun playing those with friends back then.

That said, I also remember Shaq-Fu on Sega Genesis that another friend had rented, it stands out as the worst fighter game that I played, so I also remember Shaq-Fu unfortunately. 

Now that  I think about it, one of my other favorite fighters was the first DragonBall Z Budokai, if only because it was so ridiculously lolzy that Yamcha was actually one of the best characters in the game. There was a reason why it took so long to unlock him.

I am not a fan of fighters by any stretch of the imagination. However Smash Bros. managed to make for a great game despite it's genre. I could play Smash all day, man. lol

Aside from Smash? Fighters Destiny and it's sequel. These are great games with a fun take on the fighting genre. I killed a lot of time on them.

Finally, my third favorite: Shaq Fu. Yes, seriously. I know it catches a lot of flak, but in my opinion it's better than any other fighter of it's time. But as I said, I don't like fighters, so that may explain my tastes in the ones I do like.

aww dude super smash bros 
such a good game super simple yet a nice complexity about it too. pretty cool 

I think are some like super smash bros, mortal kombat, Shaq Fu, Street Fighter, Dragon Ball Z Budokai, Soul Caliber, Tekken and many others, but I choose Street Fighter the best fighting game ever

Street Fighter 2 was the first fighting game I've ever played if not the first game I ever played so I have lots of memory's playing that one  I also remember being shocked when x-men vs street  fighter came out. In the 90's the x-men and street fighter was my favorite franchise's out there so  seeing them fight was very unbelievable at the time. 

Super Smash Bros was the first fighter that perfectly mixed platforming and fighting in the same game, but for a traditional fighter, Mortal Kombat 2 is just too good to pass up, as well as Ultimate Mortal Kombat 3

I have a couple worth mentioning. Since you said we can have runner ups, I actually have more than one.

- The first one is the first fighting game/series that I have ever played, and that is Tekken for the Playstation. My favorite game from that series would be Tekken 2 for the PSX. This game would probably be my most memorable fighting game.

- My next game would be one that a couple people have already mentioned...Super Smash Bros for the N64. I never thought Mario, Luigi, Link, or Kirby could have the moves that they do. And I'm talking strictly the SSB for the N64 and not any of the other SSB games.

- The last one I'll mention is Killer Instinct for the SNES. It was also my favorite game for the SNES...not just my favorite fighting game. This game was like Mortal Kombat on steroids it seemed to me. I loved all the combos it had.

I'll stop there but I could go on and on about other memorable fighting games.

I would have said Mortal Kombat fighting against Goro huge tough beast and Shang Tsung morphing and Street Fighter going against Bison. But when I came to vizzed and played Street Fighter III series played Gill I was like they made a fighter like that my goodness it took me awhile you have to be a very skilled fighter to play Gill no mistakes.