After all this time, I finally got to post this. I tried to do it a few days ago and it came up pretty lenghty, but thanx to mofo Glitchspot all that got lost and I got pissed off real bad. 
Now that I've chilled about that, here I am again and while it's not like the previous one, I think it's kinda decent.
First of all let me clarify this MGS "countdown". It's not a real countdown because I couldn't make up my mind about most fights as all of them are pretty memorable or epic and ranking them was no easy task as I initially thought L
So instead of giving them a proper coolness Rank, I'll just post them in the order you'd find those battles in the whole MGS saga. I know it's kinda lame but **** it, here they are:
Cyborg Ninja - The original cyborg ninja a.k.a. Gray Fox a.k.a. Frank Jaeger. I remember being really afraid of this fight after what I saw in the hallway scene and seeing how the first minutes were hell as I didn't do any harm. The guy is so badass that your shots never get to the target... but I figured it out and dumped my guns. Fighting like real men, mano a mano in this memorable fight with the original Ninja badass.
Psycho Mantis - This fight was an epic win for Kojima, and it turned out being one of the most memorable fights for any MGS fan. The fact that you can't defeat this guy without "cheating", and the neat stuff Kojima chose to throw in (HIDEO wtf?? ) would make me chose Mantis as the number one fight, even though many would disagree. To support this, I can say that there's been countless topics on many forums about "what did Mantis say to you?", thus my "choice". And he's also the only Foxhound member besides Ocelot to appear on the sequels.
Metal Gear REX - REX is probably my favourite MG ever. I remember dying a lot of times the first time I faced that kick ass mecha. And when you beat it... you have to face it again!! Damn it!!
Fatman - When I saw Fatman, I thought he was the lamest Dead Cell member, I mean a fat guy in skates doesn't appeal my tastes, but in fact he's a really good character. His fight gives you that rush feeling when you have to disarm those bomb in a pretty tight time, 4 bombs is no joke considering the are you fight in... Look!! Your favourite... explosives!!
Harrier Fighter Jet - Some of you will probably disagree with this one. Originally, I thought of the Hind D, but truth is the Harrier fight took the Hind D concept and pushed it even further. Hind D had like 2 attacks only and this one has more, not to mention that missile barrage that probably owned you a couple times.
Metal Gear RAY - This fight was quite easy, but it was epic as well. Not only you have to fight 3 RAYs at the same time, the ****ers just keep coming and coming and coming. When I did the Euro Extreme run, I could only pay for it to end. 25 of these ****ers was really exhaustiating, so I don't understand why people keeps saying Raiden is not a badass.
The End - This fight is probably the most epic I can remember. When I got to that forest I thought it was going to be a simple Sniper fight, like Wolf's. But damn, I was wrong... The first time I faced him, the fight was on for about 30 mins... and tbh I got owned big time. Second time was about the same time with the same results. Third time was longer IIRC but the outcome was finally a win for me. I agree that once you know what to do, it gets quite easy, but I bet everyone of you will remember the first time you fought The End.
The Boss - The Boss is badass, no questions about it. When you face her you gotta be extra careful because she uses the best gun in the game and damn she can use that thing. IIRC she uses that thing to shoot your shots so it's kinda hard to hit her. And not only that, if you see her run for you, you better run away if you don't want your ass CQC'd, at least 'til you learn how to Counter CQC. BTW, I love to watch her owning Big Boss during the whole game, she's as badass as it gets.
*Salutes grave*
REX vs RAY - Just like Mantis, there has been countless topics about REX vs RAY, many said RAY because it was designed to beat REX, and some others (like me) said REX because that mecha was something to fear... well, this fight ends that discussion with an amazing battle. It almost reminded me of the Jehuty vs Anubis fight because it was practically the same concept, 2 mechas settling down which one is the most badass. And while I can agree RAY had more potential, REX ownz.
Liquid Ocelot - The Ultimate fight, a fight that goes through the 4 chapters of this saga to commemorate its end, from Solid Snake vs Liquid Snake to Old Snake vs Liquid Ocelot. This fight is not that complicated but once you see the first fight "scene" you can't help to go "awsomeness".
Special Mention:
The Sorrow - This "fight" is worth mentioning because, well... if you've played MGS3 you'd know why is it so special even if it's not a real fight. Walking through the river full of dead souls and aal that creepy scenario makes this one hell of a "fight". BTW, I'm ashamed to say this, but this is the only MGS fight ever to make me look for a walkthrough as I never figured what I was supposed to do 
DUN DUN DUN DUN!!
That's it, some of the most kick ass battles you're going to find in MGS, but I gotta say that if you rather have some other fight instead, I wouldn't complain about it as every single MGS boss fight is pure awesomeness 