The Kong ones are always the best though. They involve a Genre Shift from platforming to a Punch-Out!!-style fighting match where you have to time your attacks and blocks. One of these battles involves you taking on an old master in an all-out kung-fu fight while on top of a floating log going down a raging river. Fucking Epic.
In the last one, you fight a sumo wrestler on a meteor as it plummets to Earth, and you have to time your punches to deflect his own until you get into a arm lock and DK headbutts him and proceeds to pound the ever-living crap out of this loser a few feet above him. Holy crap!
The final battle with the Cactus King/ Ghastly King. DK fights this twenty-foot tall ape/demon/tree/thing by first deflecting its mount's fire and beating the tar out of that, then the real fun starts. This thing slowly and ominously wanders towards DK, viciously smashing him with powerful attacks if he gets near. DK must wall jump over him and grab the back of his head, whereupon he hurls this thing against the wall and proceeds to smash him. With so many ways to fight this thing and it proving a very dangerous foe, even if you know what you're doing, it is great fun all around.
There's Mad Jack, the laser shooting, invisible turning hopping freak. In a box.
The giant King K. Rool cutout. The only way to beat him is to jump into a cannon and launch yourself at him. The way he yells whenever you hit him is funny enough, but hit him enough times to make his limbs fall off? He whines and faints dramatically.
For sheer epicness, we have the second incarnation Dodagon, the one that Chunky has to face. Forcing you to become giant for parts of the battle? Cool. Having one attack that's unavoidable (but is only used once), forcing you to plan ahead? Ooh, tricky! Sending the entire stage sinking into the lava after you've reached a certain point, forcing you to finish it off quickly? DAYUMN! What makes Chunky's fight with the Dodagon even more awesome is that instead of picking up barrels or some other item and throwing them at the boss to hurt him, when Chunky turns giant he actually gets to punch the boss in the face! REPEATEDLY!!
Although it's not as epic as the examples aforementioned, the fight with the giant blowfish, Puftoss, is a very fast and funny fight, dodging the boss attacks while passing across the DK signs before the time expires.
The final boss battle in Donkey Kong Country 2 with Kaptain K. Rool is one of the more awesome boss fights in the SNES Donkey Kong Country trilogy. Kaptain K. Rool is as ruthless as a final boss should be, and has the awesome music Crocodile Cacophony to really set the mood. You constantly have to be on your toes for his attacks - the spinning spiked balls, the clouds that cause interface screws, and a tied-up Donkey Kong falling between each phase all make for one tough final boss. The last phase dials up the difficulty again as K. Rool turns invisible and teleports throughout the small boss area, where it can be easy to get sucked in by his gun's vacuum attack. After the last hit, he looks like he's about to get back up, but then Donkey Kong breaks free from his bondage and punches K. Rool right out of the flying croc into the shark infested water around Crocodile Isle. Any player will likely have a great sense of accomplishment after defeating such a difficult final boss.
The rematch in the same game is enthralling in its own way because it's a really difficult fight that ends after only one hit. It's basically the opposite of the monotonous boss fights that are easy but take forever because the boss has lots of HP.
Almost all the bosses in the game are awesome due to the epic music. Listen to it here.
Mole Miner Max and Mangoruby in Donkey Kong Country Returns. The former is fought during a very intense minecart pursuit where his minions have to be negotiated first in Whack-a-Mole style. Mangoruby opts for a more cerebral battle in a battle field as colorful as the boss himself (who, mind you, becomes more pervasive and vicious the more times you hit him). Amazing.
In the same game, Colonel Pluck, a chicken who is also a Mad Scientist and fights you in its personal mecha. The fight has two stages, the latter of which has Dr. Eggman written all over it. The fact that Pluck's theme, Feather Fiend, seems to be channeling Dr. Neo Cortex only enhances the fun of this fight.
Donkey Kong (Sr., aka Cranky Kong) himself beat all of these guys out by at least a year in Donkey Kong '94. So you've gone through almost 100 levels of Lock and Key Puzzles, barrel throwing, and Donkey Kong Jr. and finally cornered him at the top of a tower. And you beat him, causing him to fall off. Time for the ending right? Wrong. There's one more level. From offscreen, DK hits the ground with enough force to alter the playfield, then you see a bunch of mushrooms flying all over the place. Then you hear a familiar power up sound. Next thing you know, Donkey Kong is as big as the big ape that inspired him! And the music is pure joy (though some would argue that the previous fight's music has it beat.