I'd like to point out that bosses that are just frigging annoying are not hard bosses. Not properly. I will not count them. Hard means challenge and difficulty through sheer virtue of you having to think. So...I'm going to cite a few good ones because they're GOOD ONES.
FFX - The two biggest deals there, bosses that deserve their position, are Yunalesca and Sin. Seymour doesn't count because he's just a dick and embarassing. He's a decoy villain, Spira's version of Dan Hibiki. ANYWAY, Yunalesca. People talk about her alot for having three punishing forms by which she gets progressively worse...and let's not forget Megadeath. That's a hard one, though the answer to handling her is to keep someone zombified the whole time. Sin also gets mention for being uhhh...THE VILLAIN, the threat to the planet by which the assault on him is not only difficult in its multi-part external battle and then flying into him to handle the rest...but it's fun and adventurous. I had NO IDEA they were gonna travel inside of him, and then...well fuck, there's Seymour again. FLICK! Dead.
DMC 3 - People are mentioning the last fight with Vergil. OH HELL YES. To explain just how bad that is, please do harken back to the first game where we see what the power of Sparda does to one of his sons when the thing is working right, blowing Mundus to hell. Vergil is one amulet-half shy of that power and the man expresses it. He's even hard with the ability to slow down time! His health slowly regenerates if you've got the difficulty up, and the times to inflict harm on him are SMALL, because Vergil is a man of speed swinging Yamato and his father's sword at once. I had to gruelingly take him down, piece by piece, for a while, because he's a swordsman of a little TOO much merit, and that's why it's a good game. Dante's brother exudes as much badass as he does!
PERSONA 4 - Inuzami. Has to be her. Not Nyx. I had Satan and Lucifer's combo spell. I reached Nyx's true arcana and then one-hit him, AND THEN I went back and did it legitimately as a challenge. Inuzami gets it out of all the Persona series for two reasons. FIRST, you have to find her. This is a game of mystery and intrigue. If you haven't explored everything and know EXACTLY how to progress to the point where one might think there was one final boss, you miss her. And THEN, there is the fight. One fight is fairly straightforward, of course, and then you learn it's all an illusion and she's much bigger, much more monstrous than conceived...and she's a creation goddess! Deadly crushing powers, and I believe she got two attacks per turn. In a turn-based battle, that's fairly significant.
SMT: NOCTURNE - Lucifer! He's frigging Lucifer in an SMT game. Do I really need to explain?
CHRONO TRIGGER - The last one was going to be a toss-up between this and Skies of Arcadia for the right with Ramirez, Zelos, and then...well...both. But you're an expert by then and you can take him. On the othere hand, there is that one battle with Lavos where you're suppose to die (after they operate the Mammon Machine). You know...where the minimum fiery rain damage is like 700-something for characters who can only have a maximum of 999? He was made uber-hard because it's suppose to be the battle to lose, but the makers of the game didn't make him unbeatable. They stepped back and said "Let's see what happens" and then gave a special funny ending to those who beat it.