His appearance in Super Metroid is unique for the game. All the other bosses have predictable patterns and specific weak points you need to hit to kill them. Not Ridley. He has no weak spots, instead just having tons of health to compensate. He's also by far the fastest of the bosses and zips around the room chaotically. There really isn't much strategy to his fight: just kill him before he kills you. This was the fight that solidified his status as the Awesome Boss of the series.
Especially noteworthy in Metroid Prime 3, where the first Ridley encounter is fought entirely in free-fall.
The Meta-Ridley battle in the first Metroid Prime is epic enough when a giant space dragon is bombarding you with bombs, missles, and fire breath. Then, you get his health 3/4 of the way down and, for the first time in the series, we get to see how Ridley fights when grounded. Turns out he can kick your ass three ways across Tallon IV.
Using the Wavebuster with a sufficient supply of missiles makes the fight much easier, although that was an oversight on the part of the developers, corrected with the PAL and Trilogy re-releases. Ridley probably ate the testers who missed that one.
The Mecha-Ridley in Metroid Zero Mission is amazing. Even with all of the powerups in the game, he remains a formidable challenge, note Mecha-Ridley's HP and attack damage are scaled up if the player has 100% of the pickups in the game, meaning he's actually easier to beat at 99% collection rate than at 100% attacking with no discernible pattern (using his attacks in any order), with a final phase that can only be described as complete chaos, with missiles and lasers firing everywhere, and an increasingly slim amount of time to fire at his weak point. Not many bosses give off such a feeling of satisfaction after beating them.
Metroid: Other M's Ridley fight is also epic, even despite the divisive cutscene before it. Samus basically shits bricks and has to come to her senses when Ridley takes out her friend. Samus kicks his ass anyway, so much so he freaks out himself and crashes through a wall. But that would be leaving out the actual fight. He plays much like the 2D games, as do you - it's fast, frantic, and awesome. It gets even more awesome on Hard mode, where almost every attack is a OHKO, even the comes-out-of-nowhere tail attack. He also does fireballs at you which cause shockwaves, tries to grab you and drag you against the wall (which he does in a cutscene in Super Smash Bros. Brawl), leaps and flies around, and is generally chaotic. Better still, you've been authorised to use the Super Missiles and the Plasma Beam literally within a cutscene of this fight, so you get to go to town with your new weaponry.
Super Metroid on the SNES, the final fight with Mother Brain. After suffering a huge attack and being brought to your knees, the young Metroid that you saved in the previous Gameboy installment which thinks Samus is its mother shows up, sucks a bunch of energy out of Mother Brain, and transfers it to you, saving your life and powering you up.
Tearjerker: The Metroid gets blown up about five seconds after saving your life. Then, Samus gets pissed.
The entire fight is awesome, from beginning to end. Unloaded dozens of missiles on its head and think it's dead? It rises out of the ground attached to a giant organic robot and the crowning music of doom begins to play. As the battle goes on and you damage it more, it starts releasing even more powerful attacks, finally leading up to that epic laser beam that leaves you on your knees, barely able to move. And then, after Baby saves you and sacrifices itself, the music changes to the theme heard up on the surface, and it sounds perfectly appropriate for the asskicking that you deliver to Mother Brain afterwards.
Quadraxis from Prime 2 is pretty sweet too, being a Humongous Mecha and all. It's a different version of the quads you've been fighting all through the Sanctuary Fortress and Ing Hive, except instead of being about your size, it's like 20 times bigger. Then it uses the Annihilator Beam against you, other forms of lasers, spinning attacks, and is just generally huge. After hitting it's weak points on it's knee joints, it is dismantled. But you're not done yet! Then it tries to repair itself, where you blast the core with beam attacks in Echo Visor mode (yeah, most of the body was destroyed halfway through the fight already) before attacking it's floating head, and THEN after that you finally hit it again a few more times by planting bombs in it's head by using the Spider Ball and Boost Ball up there. After that you're finally done, where the head flies around and destroys everything else, and Samus makes a Three-Point Landing from morph ball mode, while the head bounces around behind her, and the Annihilator Beam appears for the taking. You literally dismantle it bit by bit, and it is epic.
Also from Prime 2: Adultform Chykka. After the hell that is Torvus Bog, a fast and furious fight with a giant mutant dragonfly is just the palette cleanser necessary. After killing the (laughably easy and very boring) Larvaform Chykka, it turns into a cocoon and metamorphoses in a matter of seconds, then bursts free. The first phase of the fight features you stunning it with your weapons, then blasting its wings off. Then, it falls into dark water and becomes Darkform Chykka, which you kill by...unloading your Light Beam on its egg sac. All the while, it spawns hordes of Chykklings to assault you.
The Spider Guardian is either a wickedly frustrating That One Boss, or one of these. It really depends on your personality; you have to be very patient and keep a cool head throughout the fight. Get frustrated or try to rush things and you will get slaughtered.
Dark Samus. Period. Any fight with her is pretty much guaranteed to be epic, what with her using your own powers against you (or, in Prime 3, the other hunters' as well), often Phazon-enhanced, and thismusic playing in the background. It doesn't hurt that it's a nice break from fifty-foot monstrosities that you have to crawl all over to defeat.
Or her original form, Metroid Prime. You end up having to use nearly every weapon and even all your visors against this monstrosity of a Marathon Boss, and some attacks formerly thought useless have some use here! (Except the flamethrower.)
Flaahgra is similar with the bombing. It is a giant monstrous fly-like plant, which attacks in all sorts of manners, and you have to flip mirrors over in order to get into the tunnels (giant vines guard the tunnels) to damage it with bombs. It is clever enough to flip the mirrors back over, and you're required to flip more mirrors on each hit. This is the first major boss in the game aside from the Parasite Queen, which was just a warm up boss.
The Queen Metroid from Other M, which definitely delivers as far as 3D boss translations go. Special mention goes to the climax, where you blow it up from the inside out with a Power Bomb while your health ticks away like there's no tomorrow..
A bit of overlap with That One Boss. While fighting it, you've also got a growing swarm of Metroids during the fight while you put mommy down. This is the first and only time in the entire game where you run into the bastards and they get killed just as you would expect; freeze 'em, and blast 'em with missiles. Doesn't seem too bad, but keep in mind there's a lot of them, and you have to switch to first person to fire missiles. So lets review: You've got to freeze one, stop and leave yourself vulnerable to the other three or four, aim at the one you froze, and hope to blast it with enough missiles before one of it's buddies takes a bite. And if one DOES take a bite. it will drain your health FAST and you probably won't get yourself free before the frozen one thaws. All the while avoiding their rampaging mother It does get better as you wear down their numbers, but dealing with them is far from easy. Still all this makes it so satisfying to watch the actual boss get vaporized.
Kraid from Super Metroid. The first time he explodes you think you've beaten him, then BAM! the real Kraid appears; where the fake Kraid is barely taller than Samus, the real Kraid is two screens tall, making for an epic confrontation that spans nearly four screens all seamlessly connected to each other while you shoot at him above a pit of spikes. And he's only the third boss!
Yakuza, the literal Demonic Spider from Metroid Fusion is both fondly and fearfully remembered. Something about a Robot Spider that spends its time either spitting fireballs and German Suplexing you... you never forget.
The SA-X. You've spent the entire game running in fear, hiding in dark corners, trying to keep away from something orders of magnitude more powerful than you. Now, it's your turn.
In spite of their brutal difficulty, or perhaps BECAUSE of their difficulty, just about any of the boss fights in Metroid Prime 2 could fit this. They can be so controller smashingly frustrating that beating any of them is almost on par with beating a Demons Souls/Dark Souls boss. Try finding someone who didn't cheer upon watching the Boost Guardian convulsing and expiring.