Transformations happen in a lot of games. Sometimes mechanical ones, like in Transformers, and sometimes biological ones, like in Kirby.
In classic action game boss fights (See the Boss Fights page) it's pretty common to see a boss transform mid-fight when a boss's health gets low. Sometimes it's the game designer's way of saying
Now that you've mastered that, you're ready for something more challenging.
It can also be used to to expose an enemy's weak point.
It can be used to challenge the player to switch strategies quickly, mid-fight.
Or it can be used to make a boss just seem more cool, because transformations are traditionally visually excellent.
Player transformations have been used in some interesting ways. There's the short-burst upgrading transformation, for example: In the Bloody Roar series (A 1-on-1 fighting game), you gain energy from landing successful hits. With a lot of energy, you can press a button to transform into an anthrophomorphic (Half animal, like a werewolf or something) version of your character. When in this state, you cause more damage with each hit and more moves are available to you, giving you a massive advantage. Your energy also decreases though, and when it depletes down to zero, you're back to normal and can't transform again right away.
The opposite approach would be with The Hulk for Sega Genesis. You start the game as the Hulk, punching down buildings and smashing policemen n all that business. When your health's dangerously low though, you transform into naked scientist, Bruce Banner, who's a lot more vulnerable. At this point, the game's not about causing havoc, but avoiding it- It turns into a stealth game and gets a lot less fun. It can happen at any time, so you want to avoid transforming.
Then there's Kirby, a game that's all about transformations. Kirby's a platforming game with a lot of different enemies- But Kirby doesn't really have any combat skills. Instead, he eats an enemy, then transforms into a kind of hybrid of him and the enemy and gains their ability. So if he eats a fire enemy, he can breathe fire, if he gets the laser enemy, he shoots lasers, there's a boulder enemy, a karate enemy, an explosion one, tornado, wheel, ice, spaceship- There are dozens of transformations and abilities to find in these games, it's pretty creative. The challenge is usually finding the right ability for the job- Like solving puzzles. Sometimes you'll need fire to ignite a cannon, or you'll need the hammer to break some blocks, or the boomerang to do something, I don't know.
This one's pretty straightforward. I'll use Ratchet and Clank as the example:
Ratchet and Clank games are famous for having a bunch of ridiculous weapons, and in the more recent ones, the weapons transform when they upgrade.
The Missile Launcher, for example, becomes the Homing Missile Launcher. The Lava Gun will shoot meteorites out of it, and the gun that turns people into sheep will turn them into giant exploding sheep.