I'll have to go with Ridley in Super Metroid. It took me about a week to actually beat him. I've read that you need at least ten energy tanks and I had eight. I fought him over and over again and started getting better at fighting him. When I did finally beat him, it took me only about three minutes. I've managed to get his pattern down and get in as many shots as possible with minimal damage. So that's part of the reason for why he's my favorite. His boss fight taught me patience and endurance in boss fights.
Also, the boss fight was simply beautiful to look at. Super Metroid was probably the most amazing looking game for the SNES and it really shows in the boss fights.
Truly an impossible question... I'm very indecisive hahaha. I also tend to judge how much I like a boss based on how awesome the battle was, so there's that.
Just Listing a few that come to mind, in no particular order.
Brave Fencer Musashi (PS1): Steam Knight, by the gods this boss sealed the deal with me for this game when he crashed through the sealing.
FF 8: X-ATM092, no I didn't google that, to this day I still remember that damned spider's name, oh good times haha.
FF 10: Yunalesca and Jetch, pretty much self explanatory, plot tension, epic music, and epic multi stage fights.
Devil May Cry Franchise: "insert any fight with Vergil/ Nelo Angelo", I'm serious, ANY!
Portal: GlaDOS, because she's a potato.
Dark Souls: Ornstein and Smough, Rekting casuls since 2011 I guess.
Witcher 2: The Kayran, I know this one sounds weak, but for some reason I really liked it. Sile screaming at you from above made everything more tense and epic.
Resident Evil 5: Wesker (Not including Uroboros form), as much as this deviated from the series' roots, there's no denying Wesker was awesome, fighting like a man instead of running away makes the fights 10 times more enjoyable. I really hated how they killed off Wesker with plot induced stupidity, but that's a tale for another time.
Resident Evil 4: Krauser, knife only anyone?
I'm sure I've forgotten a lot, but man you got me swimming in a tub of warm nostalgia now, thanks.
Nyx from persona 3. Not only does it have the most epic boss music of all time in a videogame, but if you don't overlevel yourself and make yourself overpowered, it's a marathon not a sprint. I don't look at strategy guides, so the first time i went up against him, it was a nail biting experience.
Quadraxis from Metroid Prime 2. He was the only giant bosses that I face that require actualy planing and explored its weakpoints (turn into a ball, roll onto its leg and bomb the joints) than to blast it away with alot of fire powers (this was before Shadow of the Colossus or rather I didn't played that game yet).
Artorias and Kalameet from Dark Souls: Artorias of the Abyss DLC are just fantastic. Amazing fun to try and tackle solo, one of my proudest moments in that game was beating Kalameet first time on my own.
Gah! Too many to choose, and I can't remember them all.
Draygon from Super Metroid for it's unusual entrance, how it attacks while leaving no easy openings, one specific move it does leaving everyone desperate for freedom.
The final boss in Sonic 3 & Knuckles for being one of the most excitingly fast, with great atmosphere and music.
The final boss in Half Life for being unique, and something I could defeat easily compared to my friends who died about 30 times because my instincts worked against it. Puts on a great show when it dies too.
The Barinade in Ocarina Of Time because of it's awesome name and all 3 patterns it does are fun to knock out. And similar to the final boss in Majora's Mask. Unfortunately, they're both fucking easy :-(
You probably won't ever see this one, but there was a special raid boss in Lineage 2 that would summon really creepy giants and make them attack through playing a big ass organ. You had to listen to the epic music to get a better chance of avoiding that awesome bastards monsters.
i'd have to say most of the bosses in the dark souls games (excluding dark souls 2 and those two cheap ass knights before gwynevere)
i really like the design of demon souls bosses, pharlax was just interesting and unique, tower knight was imposing and really scary to fight (he made me wait a few minutes just trying to think of how to attack him) that fat guy in shadow island, not because he's hard but because he looks intimidating
and king allant because F*** him he's cheap but rewarding
dark souls there's a few but they're all pretty much the same but memorable
dark souls 2 has some interesting fights but by god do they fall short with almost every boss
none of them had any charm, last giant while interesting just had nothing to him, pursuer was just random, dragon god is just wtf
The first one that comes to mind is the "Tower Knight" from Demon's Souls. Being honest it is not that impressive, nor unique, but I really enjoyed playing against it, and It set the tone for what was coming.
Boss fights are some of my favorite parts of games; especially those with health meters. Dunno why, guess I like having a definite indicator of how much damage I'm doing to the boss.
Now, let's see...
Jean Bison from Sly 2: Band of Thieves
Pretty much every boss fight from Kingdom Hearts 1 and 2.
Mr. Freeze from Batman: Arkham City
Malthael from Diablo 3: Reaper of Souls
Wheatley from Portal 2
Multiple, MULTIPLE bosses from World of Warcraft (Lei Shen, Garrosh Hellscream, Malkorok, Madness of Deathwing, Lich King, etc.)
Really, too many for me to list here. Not a lot of games have what I'd consider a 'real' boss fight these days, though?where bosses are meant to TEST you, not act as enemies that happen to have a bit more health.
Mr Freeze from Arkham City.
GLADOS from Portal
Yami (the dark lord) from Okami.
Memorable boss fights for me are those that make you use every skill you got in the game. Those that get reduced to punching him harder than he punches me, or hitting his only weak spot does not qualify as memorable...
Xemnas in Kingdom Hearts II. That one had a lot of great bosses but that one took the cake. A bit on the easy side, but since it's a four-phase marathon I sort of understand why, and his last form is still a beast in Critical mode. 'Can you spare... a heart?'
More recently, Darth Malgus from SWTOR, the original 'final story boss' of the game. There is no other fight like it in a MMORPG, though I really wish that they'd kept the original finale of having to use knockback effects to blast him into the reactor core pit. They even gave everyone knockback-inducing grenades for the fight and people still complained that it was too hard to do! I suppose that's another first for me- the only time I've ever complained about a boss being nerfed. Should've at least kept it in for Hard mode, which requires good coordination anyway.
The 13th Colossus. Nothing else really comes close. Apart from being an awesome dragon-snake thing, you fight it by having your horse gallop at full pelt alongside it, then leaping from the horse's back onto the dragon's wings. It's a rush unlike anything else.
For starters, I enjoyed the hell out of every boss in Metal Gear Rising: Revengeance.
Shadow of the Colossus had a few irritating one, but most of them were pretty fun.
Ninetails from Okami was one of my favorites.
The No More Heroes games had some great bosses (except Jasper Batt Jr, fuck that guy)
Cynthia from Pokemon Platinum can be difficult, but she still in one of my favorite champions
The Terror from Beyond in Star Wars: The Old Republic. You and 7-15 of your buddies vs Cthulu. Godd luck.
I'd probably go with either Armstrong or Monsoon from Metal Gear Rising. I don't even think I can explain why, they are just really fucking awesome to me. The music plays a big part, but they are just so satisfying, and require quite a good amount of skill and timing to beat.