I have go with SF2 Chun Li.
The guy in the background choking the chicken is classic.
The dead forest in MKII is also memorable.
A.D. 2172 (GGXX AC)
Frasco (GGXX AC)
both of them are epic
Possibly Ultimate Rugal’s stage on Cvs2, I felt like the world was on my shoulders when I first played against him when I was a freshman. Many fighters don’t do that anymore. Plus nominee for best fighting music for a boss ever.
A.D. 2172 (GGXX AC) - Simply because of all the dead dinosaurs in the background and the flames…man thats epic just like Hecatom said.
Zero Stage (KOF2001) - Seing that man again and even more cheaper than before was WOW
The Fetus Of God (Vampire Saviour) - Seeing Jedah descend upon the stage you feel the oncoming rape…
Man… I have to nerd out here. I love good stages in fighters, something that really has been half assed in newer fighters unfortunately.
FF1 Tungfurue stage, this stage ALONE hooked me into fatal fury. I can still remember being awed looking at that rain animation.
Samsho 2(or was it 1…?) Haomaru’s stage with them waves breaking over beach.
Samsho 4 bamboo forest. When I think of samsho 4 that stage always comes in my mind.
AoF1 Jack’s stage, I think it was in a bar. AoF’s back alley type stages were all good.
CvS1 Arcade stage, (hidden)Sagat stage and Nakoruru stage. They looked great plus had the greatest music of svc/cvs crossovers.
FF3 Paopao cafe #2 aka Bob’s stage. This place’s just damn cool.
KoF 96 Psycho soldier stage? The one on top of buildings. Not really fan of KoF stages otherwise.
Project Justice Taiyo high. Nothing like jumping 5 stories in air and being able to COUNT in comparison to school building that I jumped 5 stories in air.
The stages of XCOA that broke down, gives an illusion of playing beat-em-up instead of a versus fighter. Also, Ryu’s stage in MVC1 that broke into bathhouse, heh heh.
Soul Edge grassy field, I don’t know why that stage looked so great then.
Advanced V.G. 2 Chiho’s stage. Great use of mirror effects on pond.
Last Blade 2 burning house - one of few times I was surprised that neogeo could display that kind of effects.
Gundamwing Endless duel, the spaceship(Mercurius). Kick ass music, parallel scrolling.
There are more but I better cut short.
Playing SSF2 in the arcade for the first time and seeing the cage slam down on Claw’s stage.
Epic.
The ski lodge in Pocket Fighter. Because there’s nothing like M. Bison/Vega whizzing along the ground to one end, and then riding a toboggan down the other end. =)
Yeah, that was a pretty cool one. That and whenever that asshole started to climb back on the cage blew my mind.
Tekken 4’s underground stage
in no order
cammys stage in ST - probably the most beautiful stage in st. love the bgm also
wolverine msh stage - really really well detailed. theres the bridge, then it becomes a raft and after u K.O. an opponent, they wash away while u jump to safety. and i also love the bgm.
psylockes stage in msh - i love the bgm and fighting on top of a street car is pretty dope
magneto’s spaceship in msh - the bgm is hypnotic.
a2 ken - cuz its in san francisco. (i live in san francisco)
a2 sakura - love the bgm and its very detailed
a2 gen - same as above. you can see the puddle splashes and your shadow.
a2 australia - homage to sf2 anime. fuckin epic!
a2 rolento - love the bgm
cvs1 forest - the best ryu remix theme ever
cvs1 snowstorm - love naks theme. both of theme
xvsf raging inferno - something about the stage setting on fire after you K.O. an opponent that just reeks of awesomeness
sf3 new gen dudleys stage - i love the atmosphere. the rain and the bgm really go well together
sf2i yangs stage - that old chinese guy in the background is hilarious. once you break the statue in the background, he gets angry then weeps. 
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That one in cvs1 where you’re in a wooden house being built and you raze it to the ground if you fight long and hard enough.
GGXXAC: May Ship
yep one of my favorites, besides this i like sakura’s a2 stage alot too. You fight in a backyard with a kid playin ggames inside.
Tekken 5: Moonlit Wilderness.
The glow effects and swaying vegetation was and is still incredible.
And the petals flying around when you move is just the icing on the cake.
NG Elena, Dudley, Ibuki, Alex and Sean stages.
All of them are just really, bright, colourful and full of detail. I just love everything about them.
I also really like
Guy’s stage (SFA)
Sakura’s stage (SFA2)
GG1 - Justice’s Stage
GGX - Dizzy’s Stage
GGXX AC - O.Sol’s Stage
Cyberbots - Falling Space Station
MvC1 - Strider’s Stage
Cammy’s stage in SSF2 is excellent. And it comes with the best SF BGM ever, too. Rog’s stage is a close second IMO.
Chizuru’s / Goenitz’ stage in KOF 96. That game had the best backgrounds in the KOF series, every one of them full of life and stuff going on. The giant stadium full of people, the giant screen showing characters fighting, the people flying away when Goenitz fights you… it’s awesome.
Terry’s stage in Garou, Jedah’s Stage in VS and Kim’s stage in RB2 (with Choi hanging from a telephone wire in the upper part of the stage) are also great.
Cammy’s stage in SFA3, love the music too.
Colony/Baiken & Anji’s stage in GGXX & GGAC.
Soul Calibur
Cervantes Stage.
In the platform, on the water, with the sunset, Cervantes’ ship, and the castle in the background.
Too cool.