In the animated film The Invincible Iron Man, the leader of the four elemental mini-bosses and The Dragon to the mystically powered Mandarin is an actual dragon, the physically dominating Fin Fang Foom, who gives Iron-man his toughest battle, where the magically powered Mandarin is defeated by reaching out to the Mandarin's host and convincing her to cut the Mandarin's power at its source, the magic rings.
In Iron Man 3, Eric Savin is the dragon to the Mandarin/Aldrich Killian. Savin is really sadistic and carries out most of the physical tasks for his boss.
In the original movie, John McClane is hunted by Karl, the hulking German, and must defeat him before he can defeat Hans Gruber, the Big Bad. Technically Karl does not die until the end, but McClane leaves him bloody and beaten before throwing Gruber off the building. Karl then emerges for round two, only to be gunned down by Al.
James Bond villains almost invariably have a Dragon:
Professor Dent in Dr. No. He's in charge of Dr. No's operations in Jamaica and is ordered to have Bond killed. When his minions fail him, he tries to do the job himself. In later films the villains would usually have mad scientists, professors, politicians etc. who aid them, and would have brutal killers to fill the role of The Dragon. Dr. No has The Three Blind Mice in this role.
Mr. Wint, Mr. Kidd and Bert Saxby in Diamonds Are Forever. Wint and Kidd are Blofeld's assassins and Bert Saxby is Willard Whyte's former right hand man who betrayed him to Blofeld. Saxby is later killed while trying to assassinate Whyte.
Australia: Neil Fletcher appears to fit the role of Dragon for his boss, Leslie 'King' Carney, through the first act of the movie. around midway through, Fletcher kills Carney, marries his daughter, and takes control of Carney's business empire.
In Layer Cake, the evil Serbian warlord has a Dragon hitman named, appropriately enough, Dragan. He makes constant threats to decapitate Daniel Craig's character. However, he does not follow the usual formula in that he spends the entire film untouchable. Neither he nor his boss are defeated.
In the Star Wars movies V-VI, Darth Vader is The Dragon between the heroes and the Emperor. In IV he's The Dragon to Grand Moff Tarkin. In I-III it's Darth Maul and later General Grievous. Darth Tyrannus doesn't quite fit the mold.
Tyrannus does, however, have quite a few of his own Dragons: Jango Fett and Grievous (again), and in the Expanded Universe, Durge and Asajj Ventress, along with various other "Dark Acolytes."
So does Vader: Boba Fett seems to be a particular favorite. Vader also had many apprentices, most notably Galen Marek (the main character of The Force Unleashed).
This shows how it is sometimes difficult to identify the Big Bad because within the story, the main characters think Dooku is the Big Bad, with Sidious just a myth or rumor to worry about. But The Dragon is anyone who is sent in front of a leader, whether or not they turn out to be the true Big Bad.
In Mystery Men, Tony P winds up playing right-hand-man to Casanova Frankenstein. Tony P, in turn, has a Dragon of his own in Tony C.
In Double Impact, Jean-Claude Van Damme plays twins who must separately face the Big Bad's two Dragons, one of which is Bolo Yeung.
O-Ren Ishii of Kill Bill fame seems to collect them, having two chief bodyguards (Johnny Mo, leader of the Crazy 88s, and Psycho for Hire Gogo Yubari) and a right-hand woman (Sofie Fatale) besides.
Elle Driver was a Dragon, since she was the last (and most difficult to defeat) former teammate the Bride had to fight before confronting Bill. She also serves as an Evil Counterpart, and a Foil to The Bride.
Parodied and subverted in The Running Man. Damien's huge bodyguard Sven seems to serve no meaningful role in the movie except as someone for Arnold Schwarzenegger to have the big climactic fight with. At the climax of the film, it looks like the two are about to fight, but Sven simply walks off (due to Damien's verbal abuse of him), leaving Schwarzenegger to crush the helpless Damien.
Prince Nuada of Hellboy II: The Golden Army has a few dragons: Mr. Wink, the Elemental, and arguably, the Golden Army, as they are FAR more durable than most Mecha-Mooks.
Paul Yau (the assassin with the shades), is Johnny Weng's Dragon from John Woo's The Killer. He gives both heroes of the movie a fight, especially during the church shootout, before being taken hostage in an attempt to break the Put Down Your Gun and Step Away situation with Johnny and the Killer's girlfriend and getting one put through his skull by Johnny himself.
Tatsu is the Shredder's Dragon in the original Teenage Mutant Ninja Turtles movies. In the first movie, Casey Jones is the one to take him on, while in the second movie, the Turtles themselves dispatch him with a "Wishbone Crunch" that consists of sandwiching him between all four of their shells simultaneously. "Tatsu" is one of the Japanese words for a... yeah, you guessed it. Dragon.
In The Long Kiss Goodnight, the film's main villain Timothy is actually the Dragon: the Big Bad is the mostly unseen Daedalus who is killed halfway through the film, after which Timothy replaces him as the Big Bad.
Fezzik and Inigo both play the Dragon earlier in the movie, with Inigo being the evenly-matched same-style dragon (think of the Mortal KombatMirror Match or Dark Link, or the sword fight with Meta-Knight in Kirby for the NES) while Fezzik is more of the giant physical challenge sort of dragon (Like a dragon. As long as I'm making Mortal Kombat comparisons, think of Goro or Motaro.)
Lola is Gianni's Dragon in Transporter 2. She spends most of the movie fighting the hero while Gianni takes a nap. But she's anticlimactically killed by a gag cactus spike of wall
The Cow from Kung Pow! is the Dragon. Well... sort of. He's not stronger than the Big Bad, but he is hilariously fast... and slightly Genre Savvy, when he rapidly kicks the Hero when they freeze in the air.
In Old Boy, Mr. Han is the Dragon for Lee Woo-Jin — his entire purpose in the movie is to absorb Oh Dae-Su's Unstoppable Rage.
The Dragon / Big Bad relationship is referenced in Unbreakable: "There's always two kinds; there's the soldier villain — who fights the hero with his hands; and then there's the real threat — the brilliant and evil archenemy — who fights the hero with his mind."
It's somewhat unclear who takes over as Magneto's dragon after Mystique's departure in the third film as there isn't a clear-cut second in command. The two top candidates would be Pyro, who is the only remaining member of the Brotherhood who was with Magneto prior to the beginning of the movie, and Callisto, who was the apparent leader of the Morlocks before they became Magneto's new Mook army. A case might also be made for Juggernaut, though he fits better in the role of The Brute.
Lady Deathstrike is the dragon of William Stryker in the second film.
Subverted in Equilibrium. The Dragon, Brandt, is set up as Preston's equal and nemesis throughout the film, but when they face off for the final duel, it turns out to be a Curb-Stomp Battle. On the other hand, the Big Bad, who seems like a noncombatant politician save for a blink-and-you'll-miss-it clue, turns out to be Preston's toughest opponent in the film.
In The Avengers (1998), Sir August has two: Mrs. Peel's clone and Bailey. Mrs. Peel kills both of them before Sir August dies during a sword fight with Steed.
In the animated film The Flight of Dragons, the evil red wizard Ommadon's Dragon is a literal dragon, Bryaugh, who is defeated by the Hero's literal Lancer, Sir Orin. Sir Orin is a knight who allows Bryaugh to engulf him in flames, then casts his fiery sword into Bryaugh's chest. They both die, though Orin gets better.
In the Richie Rich movie, chief of security Ferguson serves as Van Dough's Dragon.
Their respective fates are also quite different. Dennis becomes Fausto's bodyguard and Renalda's lover, Miss Purdah is very clearly killed during the estate collapse, and Eldona's fate is uncertain. She doesn't appear with Alvin in the news report, so she may have died in the estate collapse. Likewise, the fact that Alvin survived also indicates that she may have as well.
Although Transformers villain Megatron is usually the Big Bad, he is presented as the Dragon in the live-action film series, specifically Revenge Of The Fallen. In this continuity, Megatron serves The Fallen as a master, and is sent on missions to enforce his master's will. The Fallen himself doesn't fight and actively go on missions himself until the climactic final battle in the second movie. However, he is killed during this battle, quite possibly setting Megatron up for the Big Bad role once again, just like all his other incarnations.
Megatron appears to be the Big Bad in the third film up until the point when Sentinel Prime's Face-Heel Turn is revealed. After that, Megatron believes that Sentinel will allow him to remain in command of the Decepticons and become his dragon. Megatron's decision to betray Sentinel and help Optimus in the final battle comes when Carly throws it in his face that his Villain Decay has reached the point where he has become nothing more than Sentinel's unwilling dragon.
Megatron is essentially the Dragon in the animated movie too, for Unicron.
In the obscure animated movie Twice Upon a Time, The Big Bad Synonamess Botch has a dragon in the form of Ibor, a giant mechanical gorilla with a television for a face. (Neatly, one of the clips that turns up on said face is of Darth Vader from The Empire Strikes Back — George Lucas executive produced this film.)
In the first Charlie's Angels film, the Thin Man serves as a Dragon for the Big Bad. However, in the sequel, he's upgraded to anti-hero status.
In the immortal classic Road House, the Big Bad, Wesley, has a Dragon by the less-than-impressive name of Jimmy, an ex-con who comes closer than anyone else to actually kicking the hero's ass for good. For his pains, he gets the film's most spectacular death.
Bennett in Commando is one of the most memorable Dragons in cinematic history. He dies in the opening moments of the movie in order to do a Face-Heel Turn and then outlives the rather disappointing Big Bad (who is only memorable in that he is played by Tony Hedaya wearing a ton of fake tan). And if that weren't enough he wears a Chainmail Wife-Beater sports a Handlebar Moustache and is made out of Crazy Awesome. If Arnie weren't in this movie, one gets the feeling that it would have been called "Bennett". Darth who?
Bolo Yeung is perhaps the actor to most persistently portray The Dragon. Mentioned above in the entry for Enter the Dragon, he plays a virtually identical role in nearly every film he's in. A notable exception is Bloodsport, where he plays the Big Bad (though interestingly there's almost no difference in his role in this film and his others, except for the lack of someone above him).
In Rudyard Kipling's The Jungle Book, Kaa (a gigantic Indian Python) apparently serves as the dragon to King Louis, an orangutang who rules over an ancient temple populated by hundreds of smaller monkeys. He summons Kaa whenever a human tries to steal treasure.
In the sequel of A Better Tomorrow, one of the mooks is a silent gunslinger with dark glasses who kills the brother of one of the protagonists, refuses to flee with money when he's given chance during the climax, and instead dies in a fair duel against the hero.
In Kick Ass 2, Mother Russia is The Mother Fucker's strongest and by far most dangerous minion, and is the one to fight Hit Girl in the final fight (while Kick Ass handles The Mother Fucker himself). It's also worth noting that she makes more than the rest of the Toxic Mega Cunts.