Are classic side scrollers ok to suggest?

• Golden Axe (Arcade)
• Altered Beast (Arcade)
• Double Dragon (Arcade)
• Streets of Rage (Arcade)
• Bad dudes vs DragonNinja (Arcade)
• Die Hard Arcade (Model 2 Arcade)
• The Simpsons (Arcade)
• Bruce Lee (ZX Spectrum)
• Teenage Mutant Ninja Turtles (NES)
• Fighting Force (PSX)

While it also has a PC release, it was on PS2 as well if you are locked to Android emulation. Melty Blood is a total classic. I am garbage at it, but it is fantastic for couch gaming with friends.

You really should get Saturn emulation running, because as far as fighting games went, the sheer variety of games on the Saturn were STUNNING.

Battle Arena Toshinden Remix
Dead or Alive
Fighters Megamix
King of Fighters ('95 and '97)
Last Bronx
Marvel Super Heroes
Night Warriors: Darkstalkers Revenge
Samurai Showdown IV
A bunch of Street Fighter games
Toshinden S
Toshinden Ultimate Revenge Attack
Virtua Fighter
Virtua Fighter Remix
Virtua Fighter 2
Virtua Fighter Kids
Virtual On

• Killer Instinct
• Primal Rage
• Soulcalibur
• DOA
• Marvel vs Capcom

Capcom vs SNK 2 ate more of my fighting game hours than any other game, with the possible exception of SF2/Turbo/Super combined. It had everything I could ever want at the time.

Soul Caliber and it's predecessor which I've forgotten the name of. Especially the predecessor, being my absolute favorite arcade fighter.

Older than that would probably be Capcom vs Marvel.

Zero Divide
Street Fighter Alpha 3
Bloody Roar 2
Rival Schools
Soul Edge/Soul Blade
Tekken 3
Guilty Gear XX (^Core+R is the most recent one, there are like 6 different versions)
Ehrgeiz (this one have several minigames and an action RPG mode that involves a lot of dungeon crawling)

I love most of these but one I don’t think anyone knows about is Bloody Roar on PS1. Typical fighter but each character could also transform into a different beast mode with a new move set. Tons of fun although I don’t think it’s aged well at all.

Actually I really like the old Dragon Ball z fighting games on snes. I can really feel the power of those Kamehameha!

Killer Instinct, arcade and SNES Killer Instinct 2 (arcade) which was kind of ported as Killer Instinct Gold (N64)

Those are my top tier without a doubt.

Bloody Roar : Primal Fury was absolutely excellent as well.

WWE 2007 smackdown vs raw! My custom character was as tall and buff as can be, had red skin, had the skill set of ray mysterio and loved hell in the cell matches.

Saturn is out though.

Why?

Classic it may not be, but every few years I fire up a copy of Oni, turn up my playlist of mid 90s mega-hits, and lay some smackdown on some terrorists.

Basically it's the spatial exploration of a first person shooter with the fighting dynamics of something like Virtua Fighter.

Probably The Last Blade 2 for Neo Geo and Tekken 3 for the PSX. The former I actually ended up playing it on an emulator but it's still worth mentioning because it's such a great gem of a game. Here are some of the super moves just to give you a taste but there's also match footage of top players on Youtube if you want. And you can also play it on Fightcade for free.

Tekken 3 needs no introduction, I think. Considered by many to be one of if not the best entry in the series.

Dunno when/how a game is classified a classic, but since PS2 is from the 6th gen, guess I have some suggestions! =D
Ultimate Ninja 5 is pretty cool, I think. Don't like the anime much, but gameplay loop still feels pretty good nowadays. Only released on PAL and NTSC-J regions, though.
Dragon Ball - Budokai Tenkaichi 2 is also pretty fun, coming from someone that also doesn't like the series it comes from.
I guess Godzilla: Unleashed could count as fighting game too? If so, I recommend it too.

Getting the mainstream ones out of the way first: 3s, Garou MotW, ST/2X, Tekken 3 (PS1), UMK3, MvC2, CvS2, SC2, KOF '98, Vampire Savior

Got it? Good. But have you played:
Jackie Chan in Fists of Fire: Strange Mortal Kombat-looking game with three Jackie Chans, but surprisingly accessible
Fighter's History Dynamite/Karnov's Revenge: Karnovember is coming! A 1994 fighting game that held up very well
King of Fighters '95: A prime example of SNK's old school style
Fighter's Destiny and Toy Fighter: 3D fighters where certain knockdowns earn you points, and first to 5 or 7 points wins
Street Fighter EX2 Plus: Arika's quirky take on Street Fighter with plenty of unique characters and mechanics
Slap Happy Rhythm Busters: Fast polygonal 2D fighter with simple controls and supers that make a rhythm action game happen
Teenage Mutant Ninja Turtles Tournament Fighters SNES: The good Turtles fighting game. Fun mechanics to learn and break.

Edit: Added videos for the games that didn't have links to a wiki

Super Gem Fighter Mini Mix

I wonder how many people played that....

Eternal Champions. Such a cool concept, a great cast of characters, and great graphics for the time. Spent so many hours playing it with my brothers growing up. Xavier was the fucking best.

PowerStone 2. 4-player full-freedom game. Think Super Smash meets WWE games, but with pulp adventure theming (including a kinda stereotypical T-Hawk-style indigenous dude) and a vaguely Tezuka retro-anime art style. That and Virtual On Oratio Tangram (which is like if Armored Core was a fighting game) were reasons to own a Dreamcast for innovative fighting games.