Probably the uber-example would be Season 1's Scorpina. Whenever she grew she went from a pretty Asian woman to a hideous scorpion creature.
For quantity, several Big Bads tie with four advanced forms. Most recently, Dai Shi has a human form, a Lowemon-ish lion armor form (with similar transformation!), a Phantom Beast King form, and an eight-headed dragon form (his true self, as seen in a carving at the beginning of the series.) He's not alone, though: Ecliptor, Trakeena, and Olympius can boast the same number of forms.
Dai Shi's sidekick Camille has three forms: human, armored, Phantom Beast General.
In the aforementioned Lightspeed Rescue, in a few cases, the monsters have to grow twice to fight the Supertrain Megazord, which is a good two or three heads taller than the average giant monsters.
Flurious gets the MacGuffin in the end, turns into something that looks like a chess piece or a Monster Pope, and freezes the planet.
Miratrix turns into a monster bird with the power of the MacGuffin of the week and completely manhandles the Rangers' strongest machines. Unfortunately for her, Ronny and Tyzonn are able to remove the MacGuffin from its place before she can finish the Rangers. (In Super Sentai, this was the One Winged Angel form of another villain who isn't in PR. Mira's counterpart Shizuka had a different OWA form.)
Kamdor...can open his faceplate to show a different faceplate. Kind of a letdown after Miratrix's transformation.
The two main Fear Cats use Flurious' technology to go from feline monsters to awesome black-armored gun-toting warriors, a permanent upgrade. In the Boukenger, the Ashu Gai and Rei used the Gordom Engines to become the Questers.
In Power Rangers in Space, the Psycho Rangers didn't have Zords, instead transforming into giant monsters, which were hideous even when compared to the typical Monster of the Week. This is the same series with Ecliptor's four forms, and Darkonda's three: standard Darkonda, Darkliptor after absorbing Ecliptor, and a powerful but insane form he mutated into after taking a strength enhancer that had been poisoned by Ecliptor for the Darkliptor incident (and separating from Ecliptor and using him as a shield once the fight went bad.) The poison seems to count as Cursed with Awesome, though: after seemingly being taken out by, but soon recovering from, the Megazords' first finishing move, he's suddenly much saner and still ultra-powerful.
Power Rangers Dino Thunder makes a habit of it, too. Mesogog turns into a monster that is very strong and separates into five. Zeltrax uses a mystical 'tree of life' and gains a second, thorny form - and as a case of We Can Rebuild Him, Zeltrax's standard form may count as the OWA form of Terrence Smith. The White Ranger clone has access to the same Super Mode as the good White Ranger, and Elsa...does returning midseason with a new haircut, and inexplicably stronger count?
The pre-Power Rangers sentai series Choujuu Sentai Liveman has this because of the "better living through mad science" ways of the villain organization. Remaining a puny human will never do, and nor will failure to upgrade a monster or cyborg form that has proven ineffective. That's why the generals all have multiple forms. As of 38 (as far as has been English subtitled) Kemp leads the pack, going from Kenji to Dr. Kemp to Beauty Beast Kemp to Fear Beast Kemp. (He got a head start, beginning the series with his "Dr." and "Beauty Beast" forms, whereas the others' "Dr. [name]" forms were all they had.)
However, the Big Bad of Jungle Fury's parent sentai Gekiranger has a doozy: Rio (lion armor guy) doesn't have the dragon form because that came from Gekiranger baddie Long. Long goes from a boyish young man to a Phantom Beast General form, fair enough. However, when he reveals that yes, he is the Big Bad, and only wants Rio to become the Phantom Beast King so he'll go out of control and destroy the world, and that fails, Long takes on his true multi-headed dragon form. And for the teamup with the following series, Engine Sentai Go-onger, Long returns and eventually possesses the Monster of the Week, Nunchuk Banki, to become Long Banki. So ultimately, he's got as many bodies as Dai Shi.
In Tokumei Sentai Go-Busters, Enter and Escape did pretty well in their from-time-to-time fights with the Go-Busters, utilizing tentacle arms and dual-guns respectively. When they start to take on the Go-Busters more frequently, they don special battle-suits but don't actually transform, since the suits lack gloves and helmets. However, when the Go-Busters bring out their Powered Custom forms, Enter and Escape finally decide to get One-Winged Angel forms, upgrading to powerful robotic bodies when they're needed. Escape goes first, upgrading to Escape Evolve in #37, Enter goes next, becoming Enter Unite in #40.
Kamen Rider Den-O and Kamen Rider Kiva had monsters occasionally assuming gigantic monster forms (dubbed Gigandeaths and Sabbats, respectively). This typically only happened when they needed to show off the newest Den-O form's Cool Train car or Castle Dran. CG costs are expensive.
Kamen Rider Black: The High Priests sacrifice the stones keeping them alive to complete Nobuhiko's transformation into Shadow Moon. He then rewards them by powering them up into Great Mutant forms and making them his lieutenants.
Some Orphenochs in Kamen Rider 555 can also take on advanced forms. There are no giant-sized vehicles to deal with them (though the vehicles they do have are quite weapon-laden and sometimes extend/expand. However, these are not typically used for giant monster-busting; more for faster or more numerous enemies, or for when you really, really want a rival Rider dead.)
Throughout Kamen Rider, there are many monsters who are humans/former humans who can power up, or are monsters hiding as humans (still this trope; hence its alternate title "Behold My True Form.") Every Orphenoch, Fangire, Worm, Dopant, Greeed, and so forth is this.
As with Super Sentai and Power Rangers above, the human commandants of the terrorist organization Shocker in the original series had monster forms.
In Kamen Rider Dragon Knight, the Mooks did this. It didn't do them much good. A flashback reveals that the advancedMooks can become more-advanced, flight-capable ones. It...still didn't do them any good, but hey, what matters is that it looked awesome. The last two or three episodes give us all three types of cannon fodder as well as various monsters in an all-out war against the Riders.
It is a tradition for the more recent Rider series (Den-O, Kiva, Double, and Oz) to have the monsters do this. The only one to break the sequence was Kamen Rider Decade (released between Kiva and Double), which makes up for it by having the good guys do it — FINAL FORM RIDE.
Kiva himself was able to do this by transforming into his dragon-like Flight Style form, which did give him a huge boost in power.
A few main human villains eventually do this in order to reach their goals. Tennoji in Kamen Rider Blade fuses himself with the artifical Category Ace Kerberos in order to try and win the Battle Fight himself. In Kamen Rider OOO, Dr. Maki absorbs five Purple Core Medals to mutate himself into a Greeed, completing his transformation in episode 42.
Invoked in Kamen Rider Fourze but on 2 different levels - the Monster of the Week Zodiarts can go into a "Last One" state, which involves adding some weapons or other bling to the existing monster suit, while the Horoscopes (Zodiarts evolved and promoted to Co-Dragons) have a "Supernova" form much closer to this trope, a hideous and always massive CG-rendered monstrous form. Also Gamou spends most of the series human until its finally revealed that he's the Sagittarius Zodiarts, assuming that form in Episode 42.
An interesting example in 'Kamen Rider Wizard. The Phantoms start as giant monsters ripping apart their Gate's Underworld, but become humanoid upon freeing themselves. Sora, a human Serial Killer, ended up doing this trope accidentally when he was used in the Eclipse Ritual; instead of being replaced by the Gremlin Phantom, he became the Gremlin Phantom.
In Spearhead from Space, the serial that first introduced the Autons, the creatures themselves look like mannequins unless tweaked to look (mostly) human; however, their leader gestates into the Ultimate Form with which to Take Over The Earth. It is... a giant, tentacled squid.
Technically, the tentacled squid is called the Nestene Consciousness, a creature with an affinity for polymers and plastics (or, if the Ninth Doctor is to be believed, the byproducts of making said plastics). The abomination described is its only form. (Of course, by the time of "Rose," the Consciousness had lost its squiddishness, and resembled a big face in a vat of molten plastic, apparently having lost its physical form in the Time War.) The point being, the Autons don't turn into it; rather, it controls plastic, and Autons are what we call the plastic soldiers under its command (at least in the old series.) Mannequins are already in the right shape to become Mooks, so that's the Nestene Consciousness's weapon of choice.
Subverted in The Satan Pit, where the Doctor finally encounters The Devil, a monstrous horned creature the size of a skyscraper, only to discover that it is only a shell, as the Beast's essence is now in a regular human.
Played straight by the Professor Guinea Pig in "The Lazarus Experiment", who winds up as a freaky scorpion thing.
Rev. Golightly in "The Unicorn and the Wasp takes the form of a giant wasp-like alien when angered.
Ganger!Jennifer from "The Rebel Flesh"/"The Almost People", who goes from seemingly human to a loping, four-legged monster.
Beetleborgs has had its share of transforming baddies. Kind of odd, given that many of the good guys were already monsters.
Noxic in the first season had a super form called Hurt-Ulyles, in one episode Fangula the resident vampire became Super Fang and in Metalix- The Crustaceons themselves have this.
In the episode Buggin Out which is a satire of the 80's remake of The Fly Flabber sees a drawing of a matter transporter, brings it to life and tests it out- but unfortunately much like in the movie a fly monster called Kombat Gnat gets in the machine with him- and when he arrives at Zoom Comics he's merged with the creature and gradually evolves into Kombat Gnat and the kids have to fight him in order to get him back to normal.
Inverted on LOST: The Man in Black/Jacob's Enemy can turn into the Smoke Monster anytime he wants, except during the final battle, since he has become mortal again.
The Wraith from the Stargate Verse have very versatile organic technology. Even their ships are alive but are restricted by their power generation capabilities. In the final episode, one Wraith got the right idea and wired the most potent energy source in the known universe into a Hiveship (Wraith equivalent of The Battlestar). It used the extra energy to grow more armor and guns, resulting in a HUGE (3200+ meter long) monster of a ship armed with dozens of cannons. Asgard plasma beam weapons which could easily neutralize a normal hive in about half-a-dozen shots barely even scratched the Superhive. Plus, the increased sensor sensitivity...
(the team is scouting the superhive with a cloaked jumper) McKay: Hold on, they're powering weapons... Ronon: They can't see us, right? McKay: No, of course not. They must be just running a test- (a shot passes VERY close) Holy crap... Sheppard: What are the odds of them randomly firing a test shot DIRECTLY AT US?! McKay: I'd say: given the enormity of space all around us, non-existent?!
They managed to take it out only by sneaking a multi-gigaton nuke inside but still.
Zogu, the Big Bad of Ultraman Gaia first appears as an angelic entity to trick Gaia and Agul, then defeat them. When round two comes around, they're ready for his tricks and beat the tar out of him. In response, Zogu undergoes the reveal your true form version of this trope and turns into an absolutely massive, centaur-like beast that can crush skyscrapers under his feet. After a lengthy fight, he's finally killed by a combined beam attack but Gaia and Agul were supercharged with the power of Earth's monsters and at their strongest at the time.