Ares from God of War 1.
Pretty much the reason behind the game, ultimate battle includes you fighting him mano-a-mano with your skills, him sending you to protect your wife and daughter against constantly spawning shadow clones of yourself, with the ability to hug your family in order to give yourself strength, followed by Ares wrenching you back into the real world, you deciding not to give up and pulling a Chekhov's Gun by using the sword/bridge from earlier in the game as an impromptu weapon against the God of War who has absorbed all your powers and is using them against you.
Never has a game gotten me so much excited, pushing me to the limit in order to defeat the final boss and exhale happily.
So, in general, I'd rate the best boss battles being those that you can't prepare for (in the game) and ultimately test the player's real ability without causing cries of anguish about the enemy being overpowered or broken.
Remember, in video games, it's all about the obstacle, but you can't be asked to jump at the level of a professional pole jumper in order to have fun, right?