Mike Tyson from Punch Out! back in the day this was an awesome fight, not as exciting now, but when I was 5 trying to beat this was an amazing and frustrating fight.
Psycho Mantis form Metal Gear Solid. Cmon, this was also insane at the time, reading your mind, moving your controller, playing with your tv. It was just awesome.
The End from Metal Gear Solid 3, totally unique and I love the MGS franchise because of the strange and awesome boss battles that occur, this is one of the best. Its not a normal fight, it can take hours even days to beat him, the unique nature of it makes it an awesome fight, if you haven't played MGS3, go do it.
Bowser from Mario 64, "So long King Bowser" is one of the best lines in all of video games, the battles weren't exactly tough, but they were very memorable.
Bowser form Super Mario World, the last battle of my favorite game of all time. I love everything about this, the music, the different methods Bowser uses to attack, everything, I love it.
Tyrant from Resident Evil, truly scary, the object is to survive but Tyrant was a scary mofo. The whole game made me crap my pants, but this battle took the cake because of me pausing the game every 5 seconds to collect myself.
Stallord and Agorok form Zelda: Twilight Princess, both were very memorable and I enjoyed them very much, both had multiple parts to the battles and all the parts were fast paced and exciting, I loved them.
Colossi from Shadow of the Colossus, they were the game, and they made it an awesome game. Each colossus was a puzzle, trying to get to the weak point and damage it enough before it knocked you away, this really was an epic game and I loved it.
I can never pick one =/