BioWare and Obsidian, the makers of some of the most popular Western RPGs of the past decade and a half, certainly know a thing or two about awesome bosses.
Baldur's Gate series
Final battle of Baldur's Gate I. Sarevok, being an extremely badass Lightning Bruiser, is so good at gibbing your entire party in seconds that when you finally kill him you'll be patting yourself on the back for days.
Baldur's Gate II: Shadows of Amn has so many of them. How about...
"KNOW ME THEN BY MY BEST NAME, MORTAL. YOU FACE DEMOGORGON, PRINCE OF DEMONS!"
Kangaxx. Immune to all weapons below + 4 and all spells, regenerates really fast and has an unlimited supply of Imprisonment.
Ol' Jon Irenicus himself. Technically, there is little about Irenicus that distinguishes him from a really tough foe. But, oh, does this show the importance of plot, pacing, and structure. You encounter Irenicus in just enough different ways, in just enough different versions, and his influence in the plot kicks just enough different dogs in different ways. Each encounter seems the last. Then, there build up to the final throwdown is nothing short of amazing. After all of that, beating him for good? It's soooooo satisfying.
And, of course, the really nasty Twisted Rune fight. It's almost mandatory when you're soloing a Sorcerer, too.
Baldur's Gate II: Throne of Bhaal picks up the awesome boss trend and runs with it...
The fight against Sendai. She's tricky, tough, and great deal of fun.
The Improved Yaga Shura mod. Thought he was a pushover before? Think again. And he brings his army with him. His entire army.
The final battle with the Ascension mod installed. True epic. The entire Bhaalspawn Five, Sarevok, and Amelyssan. And you have Bodhi with you, or Balthazar (and he's replaced in the Five by Gromnir).
Ascension converts the final level from a relatively simple marathon fight against Mellissan into a Boss Rush of epic proportions. The first indication the player has of this is when instead of ending her A God Am I speech at the start by attacking the party, Mellissan dismisses you as beneath her notice then resurrects Irenicus and Bodhi and sics them on you. Then for extra Kick the Dog points she turns Imoen into the Slayer, leaving the party to scramble around trying to stay out of her way until she snaps out of it (unless you're a heartless bastard and just kill her).
Additional mods that are Ascension-compatible allow for things like recruiting Irenicus (think about it, you can have both games' Big Bads at your side in this battle, if you're the good type even having redeemed both), temporarily resurrecting several plot important characters from the past to fight at your side (including Gorion and Yoshimo), oh, and Demogorgon also shows up again. Bad luck for him that he just stepped into the sphere of Bhaal, where you can destroy him for good. This all combines to make the final battle into an ultimate showdown of ridiculously epic degree.
Planescape: Torment has, as its approximate halfway point, Ravel Puzzlewell. The environs the fight takes place in are suitably creepy, and the preceding conversation has established her as nothing less than an outright Manipulative Bastard. She also summons giant, corrupted tree-things to do her bidding, and her spells are nothing to sneeze at either.
There's also the NEXT big boss you face after The fallen angel. It actually radiated power. And after you beat him, he's still not dead yet, and he says that the both of you are at such low power compared to last time you met.
The final boss, who is the titular character's own mortality given physical form. You don't have to use anything but words on him.
Ah, but what epic words. Listening to the smug bastard's endless gloating as he outlines everything that brought you there, then sending him reeling with one sentence as you throw the Arc Words in his face. Even with his next lines being just text, you can hear the fear start to creep in there.
While opinion may be divided on whether or not Neverwinter Nights 2 is a great game, the Final Boss and the penultimate boss fight are almost universally agreed to be awesome. First, each of your party members are tempted to the Dark Side in turn, with their acceptance or rejection based on first their alignments (Good characters never turn) and then their loyalty to you. Many speeches are given, and affirmations of loyalty are made. Then you beat up The Dragon and whatever allies he has. Then the real Big Bad comes through the portal, and he tempts YOU. Then you beat him up. In both cases, you have your entire party fighting—some six to ten level 20 characters. If you go to the Dark Side, you and maybe one other character have to fight your surviving party members while the King of Shadows watches. This results in a Bad End, of course.
Darth Malak, anyone? The most powerful enemy in the game, alone, clashing with you in a lightsaber duel while aboard his fortress in a manner not unlike Luke vs. Darth Vader in Return of the Jedi. The emotional impact behind this battle - Revan, fighting his/her old apprentice to either redeem him/herself or claim Sith Lord supremacy - combined with the fact that it's a friggin' lightsaber duel has to make this one of the most awesome fights in video games.
Facing off against some of the Sith teachers on Korriban. Not quite as epic, but almost as fun. Depending on how big a bastard you want to be, JorakUln can lead to fun times with lightning bolts for one of your douchebagfellow students. Or the final encounter with Yuthura and Uthar — depending on whether or not you went for the straightforward option, the double-cross, or the double double-cross, it can range from a truly kickass Dual Boss fight, a Mêlée à Trois, a two-on-one fight with optional backstabby goodness, or an honest-to-God heartwarmingHeel-Face Turn. Ah, choices, choices...
The temple-top fight against Bastila is a jaw dropper, too. Massive Player Punch for a light sider male.
Darth Traya in the second Knights of the Old Republic. You think you've won, and you would have, except for the three floating lightsabers Traya summons to kill you.
And then there's her dialogue. By TV Tropes definition she may be a Nietzsche Wannabe, but if Nietzsche were a Jedi, she'd have convinced him to curl up and die a long time ago.
The boss fight against Atris. No, not near the end, when you first meet her. It's a war of words where every self righteous comment she makes can be thrown back at her, to the point where she flies into a rage and declares that you should have died, before being called out on her loss of control. Then your light and dark side points are tallied up.
It may be a Game Mod, but Brotherhood of Shadow for KOTOR 1 has some whoppers. The first is a battle against Akirakon Sin, an ancient Sith warrior. He then forces you into a Mirror Match, followed by spawing identical copies of himself and all of them attacking you. Then there's the insane Echani Jedi Solomon who has become ripping Drunk on the Dark Side and is just as bad as you'd expect. Then, you get sent back to deal with Sin, and he throws you through a series of fights, including Mandalore the Indomitable in orbit over Malachor V!
Considering that he was using you as an Unwitting Pawn the entire game? Considering how callously he talks about his lost family, especially when you've got Dawn Star right next to you? It is very satisfying to pound Sun Li into the ground. If you're fond of little Wild Flower, it is also terribly satisfying to kick Ya Zhen to the curb for terrifying the sweet little girl.
In general, the Mass Effect series doesn't have a lot of bosses. Some levels may end with fights against named characters, but in practice these are just named Elite Mooks for a Boss Room. That said, when the series does give a proper boss fight, it tends to be epic. The proof? The below is basically all of the series' true boss fights.
Balek of Bring Down The Sky forces you into a Sadistic Choice, let him escape or blow up the hostages. Choose the latter and after his boss fight you can kill him, repeatedly shoot him, and/or leave him to be taken in alive.
Let him go, and in Mass Effect 3, he comes back. You can kill him or have him give the Batarian fleet to your command.
The final boss of Mass Effect 2: Human-Reaper Embryo. You fight a REAPER. On foot. Even if it's just an incomplete one, that's still one of the most awesome things in the entire game, and it's fought to some of the most awesome music in the game. Killing the Human-Reaper Embryo pretty much confirms that yes, Shepard is the only one who can save the galaxy. It also looks like the T-800 from Terminator after its skin has been burned off. Reduced somewhat if you hit it with the Cain, a boss-killing mushroom-clouding explosive launcher that halves the boss' health if you hit it. (Which is more like taking off 1/4 of its health on the hardest difficulty.) Then again, using the Cain means you kill a giant mecha-Chtulhu with a nuclear bomb in the face. Think about it.
Though it's more of a mini-boss, taking down a thresher maw, whose main strategy for defeating it is to, according to the Alliance, use heavy ordinance like TANKS or, according to Zaeed, "Run the f**k away in the other direction" on foot when the mission only requires you to survive it for 5 minutes is a Crowning Momentof Awesome, especially on Insanity difficulty. Even the krogan think so! If you manage to kill it the Krogan want to mate with you.
The Geth Colossus during Tali's recruitment mission. Three different ways to attack the damn thing, with geth closing in on you constantly from every angle, and Tali's theme music blasting in the background.
Tela Vasir in Lair of the Shadow Broker, at least for Vanguards. Vasir can use the same Biotic Charge ability Vanguards have, so much of the battle involves zooming around the battlefield like crazy. Even if you aren't a Vanguard, it's still an awesome fight. Also counts as That One Boss.
The fight against The Shadow Broker himself also fits here.
Samara's loyalty mission has you try and get space vampire Morinth to seduce you (not easy if you didn't do some background research). Then you have to resist her mind control. Fail this and Samara comes in to save you, killing her own daughter in the process.
Kasumi's loyalty mission where Hock is in an invincible gunship. She climbs up a structure, runs for Hock and jumps on the ship while in flight to take out it's shields, before taunting him and jumping a hundred feet to do the splits as she hits the ground.
Mass Effect 2 has a slaver who holds planets ransom where he will release prisoners if he's not paid. Shepard calls him out on this then proceeds to blow him away.
Recruiting Garrus. You fight off three of the best mercenary gangs, kill their leaders, and take out a gunship. Even better with the sabotage you can do before/during the attack.
In Mass Effect 3, the Reaper Destroyer on Rannoch. Again, it's not actually that hard, but you're facing down a goddamned Reaper. It's amazingly epic and a fitting conclusion to the Rannoch arc. Shepard paints a target on the Reaper while charging around like a ADD kid on Red Bull to avoid it's laser.
The one on Tuchanka is also pretty epic. The Reaper is blocking the way to the Shroud facility, and the chance to destroy it conventionally has been lost. Instead, you have to run towards the Thresher Maw hammers, and dodge the attacks of the Reaper and the numerous Brutes that are aiding it. Once you activate the two hammers, a huge Thresher Maw called Kalros, described as the mother of all Thresher Maws, is summoned to battle the Reaper and wins.
Kai Leng. After dealing with this slippery bastard throughout the game, it's satisfying to finally lay into him with all your might. Then, after you beat him, you get one of Shepard's best Crowning Moments of Awesome.
Shepard:That was for Thane/Miranda/Kirrahe, you son of a bitch.
While not technically a boss, the final charge against Harbinger was pretty awesome, being the closest thing to a final boss the game has.
Citadel's DLC final boss is your clone. It's the same class as you, and will use mostly the same powers you have. Yes, that means a Vanguard clone will charge/nova you. Who didn't charge at your clone as a Vanguard after s/he charged you?
The same DLC also has the trilogy's final Bonus Boss: the Armax Arsenal Mirror Match which throws you against all six player classes at once, resulting in you having to contend with every class's gimmick simultaneously. Dodging Vanguard charges is even more fun when you have to worry about the Sentinel spamming incinerate and that Infiltrator who disappeared when you weren't looking at the same time.
The Ogre in the Tower of Ishal. It's not just a Wake Up Call Boss, it's an awesomeWake Up Call Boss. Especially if you're playing a melee character and you get the final blow against it. You leap at it in Bullet Time and stab it to death, tackling it to the ground.
The Fade Dream in the Circle Tower is a Scrappy Level to many, but it does have the final boss against the Sloth Demon. It almost seems like the Smug Snake Demon is getting more and more desperate as he changes forms in a vain attempt to defeat you.
The battle against Zathrien. Fighting a powerful and decidedly notSquishy Wizard consumed by his rage and grief over a centuries old crime who casts some of the most powerful spells in the game and summons Ents into battle? While epic, it's the aftermath of the battle that's really awesome. The boss music is icing on the cake.
The High Dragon. Unlike the other Dragons who can be taken down fairly easily Flemeth is stationary and the Archdemon is made easier with the support of an army and ballistas the High Dragon will have you on the edge of your seat. One wrong move and you're dead. This battle rivals the Dragon battles in the Baldur's Gate and Icewind Dale games for their sheer awesomeness.
The Archdemon isn't as challenging in terms of gameplay as one might hope, but the scene is epic. Fighting a demon-possessed dragon god and its army, with YOUR army including various characters you've helped along the way, on the roof of a burning fortress at night during a thunderstorm, with ballistae.
Dragon Age II has a few. The Harvester, the High Dragon, and Knight-Commander Meredith all have moments. The Duel Boss with the Arishok is cool, if more difficult than the group fight.
The DLC boss Corypheus is an incredibly epic battle, given that he's one of the Tevinter magisters who tried to enter the Golden City and one of the first Darkspawn.
The other DLC, Mark of the Assassin, offers a couple more. The first one is the Alpha Wyvern, which can only be summoned to kill if you've gathered all different kinds of wyvern bait and poured them all at once in one big pile while proclaiming you will take a trophy that will become a ballad material. The second is a Dual Boss - Duke Prosper riding his very own pet wyvern Leopold, firing explosive arrows at you and sticky grenades that act as bullseyes for the wyvern. It ends with Hawke dodging Leopold's attack at the last second, sending it along with Prosper off the cliff towards their deaths. You even get the chance to taunt the duke both before and after he falls and breaks every bone in his body.
In the main game there are climactic battles at the end of each chapter. Moscow provides the best in and of itself as you close in on Konstatine Brayko, American 80s obsessed Russian mobster who just got done torturing one of your allies. When you get to him, he's on a disco stage and the two of you engage in Pre Ass Kicking One Liners set to a rousing guitar riff. When the battle starts, you realize it's Autograph's "Turn Up the Radio" (they originally planned to use "The Final Countdown"). As soon as you manage to drop to drop his health by a quarter, he shoots up on cocaine and comes at you with a knife. Accepted wisdom for this segment is to RUN until his high passes.
Dungeon Siege III is full of these. From the fight against Rajani (another archon) who sets most of the arena on fire, through the Warbeast battle - a humongous monster in a mine, with enemies pouring in and friendly cannonballs exploding everywhere, the Dapper Old Gent, all the way to a 5 stage brawl against Jayne, the penultimate stage being a 2vs3, where the bosses combo your ass into oblivion! Hands down the best Obsidian boss fights.
Fallout: New Vegas has very few traditional bosses, but the Giant Roboscorpion from Old World Blues is suitably epic. It's the size of a semi truck, has multiple attack modes, and — importantly — is fought in an arena that gives you multiple options on how to defeat it, depending on your character's strengths. Also, its onboard nuclear reactor goes critical after it's defeated, giving you a nice mushroom cloud finale.
Legate Lanius, who is the Final Boss for three of four endings, at least should you choose to not try and talk him down. Depending on the option you take, it is possible to end up with him and you going at it in single combat (best done with a melee weapon of your own), or with you trying to do this while he is sending hundreds of goons after you. The options and ways to take him down are endless, and the fight's even better if you're deliberately forgoing the Powered Armor to fight him while on weaker terms.
Even better since the release of the DLC Lonesome Road. You can battle Lanius, who wears legionaire armour and wields the blade of the East, while wearing the Duster of the Courier and wielding the Blade of the West. East versus West in epic battle.
The end fight of Lonesome Road, when you have to fight wave after wave of the Marked Men. If you talked down Ulysses previously, he'll fight by your side too.