All time.  It would have to be "The End" in Metal Gear Solid 3.  I have never played a boss battle quite that insane as far as gameplay, strategy and entrenching.  I mean that game really just blew my mind as far as how surreal everything felt...and it was on the PS2 which at that point in late late 2004 was starting to show its age compared with the GC and Xbox.

"No boss fight can best The Boss."

Rex vs Ray was epic.... I'm a mech lover so i loved it. Gundam developers should take some notes on how mech should move

I would have to say that The End battle is pretty epic.  In fact, that whole game is something else. My favorite of the four "Solid" titles. Anyway, I couldn't think of any other battle that could really compare. I'm pretty sure it's the only boss battle where you can still use stealth to sneak up on your enemy and take them out. Fantastic. Simply fantastic.

Decoy Octopus...

But in all seriousness. I have never had such a feeling when fist fighting "Liquid" Ocelot in 4. When they stabbed each other in the neck, then the camera pans around, and there health bars fill up.... Epic. The next two would be Rex vs Ray, and Psycho Mantis in 1.

Psycho Mantis for the win :)

MGS - P. Mantis
MGS2SOL - Fatman
MGS3SE - (... This... is) The End
MGS4GOTP - Ocelot

MGS1: Psycho Mantis
MGS2: Solidus
MGS3: The Boss (CQC that mother lol) and The End
MGS4: MG Ray and Liquid Ocelot

The Boss

psycho mantis, liquid ocelot, or the boss
honorable mention: shagohad, rex vs ray, volcan raven, fatman, the end

Fighting Liquid Ocelot with the ocean backdrop in MGS4.

"No boss fight can best The Boss."

The final battle in MGS4.... no words can describe it. Ok maybe one word... and that's EPIC!

The End, Psycho Mantis, The Boss, and The Sorrow. I especially enjoyed the Sorrow because I killed nearly every person in MGS3 with the knife by slitting their throat, so all the ghosts were people bleeding from their necks. It looked hilarious. XD

I really liked solidius at the end of mgs 2 because of the blade fight.

Sniper Wolf for me.

Overall my favourite is definitely Psycho Mantis. 
At the time that thing blew my mind...it's basically the fight that hammered home the message to me that videogames could be more than just interactive movies. 
Kind of showed me that videogames are a form of art that can do things that no other forms of art can do. Using the console in such a weird way to reach out to the player and disorientate you in the way that Snake would be disorientated from the fight. 
Pretty damn clever.

" I think I'd have to go with Sniper Wolf, eventhough it was a nightmare when you first encountered her, having to walk back on yourself to get the sniper rifle. "