Like the title says. I will name off some of my Favorites....

Jenova Absolute

Everything about this broad's existence terrifies me. The creepy psychological hold she has on her "children". Let us not forget that when Sephiroth is on the run he likes to leave severed pieces of her behind.......that turn into giant freak show monsters!!!!! Her music was just as haunting. You get to fight her several times in the game and everytime she makes me scream "Why won't you DIE!!?!?!"

Sephiroth Arena Battle (KH)

Oddly enough my probably favorite Sephiroth encounter isn't actually in FFVII or it's direct spinoffs. It is in KH, where you face off against this timeless bad ass. He gives so much smug charm and insanity in that battle. He flies around the battlefield with me running around terrified for my life. Then I seem him performing that god forsaken Heartless Angel move so I am frantically trying to get to my Sonic Blade throwing move to keep it from insta-killing me. Such an intense battle for sure. There has never been a battle more satisfying.

Kuja Trance Final

The last encounter with your Zidane's fanatical brother is so epic. The way the music starts, the camera slowly focuses on Kuja, in all his Trance glory. Over all I think the thing that makes this fight so special to me is the story behind it. Kuja was basically having a temper tantrum because he just found out his life was purposely made finite as not to crowd his superior younger brother......and he wasn't ready to die. Its pretty horrifying to think of someone so young (Kuja must of been something like 18) to find out they are terminal. He didn't want to go down without a fight tho, and boy did he put up one. Flare death for everyone, all the while looking so elegant.

Zack's Final Battle.... (Crisis Core: FFVII)

Uhg, this fight makes me teary eyed just thinking about it. This fight is not difficult at all, it is mostly meant as a story plot device, but boy was it emotional and perfect in every way. Anyone who played FFVII probably knew Zack's short lived story. Even with so much forshadowing to that very moment, I still didn't want it to be over. You come to realize that he had SO MUCH to live for, and he was such a straight guy. His theme playing in the background ..... as you watch Zack use every ounce of strength in him to fend off what seemed like hundreds of soldiers by himself.......until finally......... he can't fight any longer.

Yunalesca

This bitch right here...........not only is she bat shit insane but also a total cunt in a half in battle. Her status effect of choice is always Zombie. Which is almost always followed by Full Life or Regan. She also makes it extremely dangerous to get rid of it because at any moment she could use an ability that insta kills anyone who ISNT ZOMBIED!!!! What kind of nonsense is that?! She is probably the most difficult storyline boss in the game if you ask me. 

Kuja's is pretty great, particularly because of how it ends. Also worth mentioning is Necrophobe in FF5.

Then again I'm just biased towards FF9 and 5.

Kuja, I wasn't taking him seriously early on in the game, then after learning his relationship with Zidane and Garland. The battle as a whole is tough because unlike in FFVII and FFVIII.....you CANNOT max your team out with all 9999HP. Amarant and Steiner get really way up there, Zidane ends somewhere in 8k I think. But the mages? They can get obliterated by Kuja's Holy and Flare in no time. And if my memory serves he does them back to back at times.

Zack's final fight is also one of my favorites. Personally, I LOVE Jenova-Life, the battle right after Aerith's death. The mood is just outstanding on that battle. Every single final boss from the main series just has an epic, memorable feeling to them (and dat songs). I'm considering Braska's Final Aeon and Kuja as the final bosses here by the way.

The battle against Belias in FF Tactics is also impressive. Such a simple game graphically, but the battle has such a powerful atmosphere. I really enjoy all the 3 battles against Barthandelus from FFXIII as well.

I'm sure I'm forgetting some great fights, there are too many of them.

Oh how can I forget about FFXII, which have some of the hardest skill and strategy based battles in the series. People love to say "Oh FFXII is automated" Let me see someone automate this battle and I will quit gaming all together....

Jenova Life is a great battle too. After just getting your heart ripped out by Sephiroth, I was mentally rampaging Jenova with my stronges abilities imagining that getting through her quickly would allow me to get my revenge on Seph faster. Such a great moment.

I also consider Final Aeon and Kuja as more befitting final battles. Yu Yevon and Necron are some of the most WTF last ditch bosses ever (YuYevon at least makes sense plot wise). To count them is to count the solo dual between Seph and Cloud at the end of FFVII the final boss fight. :P

These guys were so badass. I know I'm probably one of the only people who like Final Fantasy XII, but they were my favorite villains out of all of the game.

You are not alone. Fighting the Judges are some of my fondest moments in FFXII. FFXII has a special place in my heart mostly due to these guys and the battle system.

I personally think FFXII has the most productive battle system in the series. The Gambit System is tightly constructed, that other games still can't copy them right. I can't help but see Dragon Age's system as a poor man's version of Gambits. They worked so well. And XII is still the only FF where I found every spell useful throughout the game. I almost never use spells like Reflect, Protect, and Shell in most FF games, but in FFXII they are essential to survival in some areas. And many debuff abilities like immobilize are crucial. I found the battles so much fun. And god knows some of those Elite Hunts are out of this world hard, with lifebar for DAYS!

Huh, they have a pretty similar design to these chappies in FF14 ^^

FF1

FFIV

 or

Fun one

FF VI Dragons

FFXIII

All the Eidolon battles in FFXIII are EPIC imho. :)