To start with, it is worth pointing out that giant robots are pretty much just superheroes in giant mechanical form. To wit, look at the original piloted super robot, Mazinger Z. It's power-set includes:
-Super Strength
-Invulnerability
-Drawing energy from the Sun
-Eye-beams
-Super breath
-Flight
It is pretty much a 50ft tall, mechanical, Japanese Superman.
On the other hand, the second major super robot, Getter Robo, is pretty much what would happen if someone built a super-robot powered by those crazy cosmic rays that gave the Fantastic Four or the Hulk their super-powers, with a touch of the Green Lantern ring power. Gurren Lagann is really just a big love letter to Getter Robo, using very similar ideas and cosmology.
In short, mechs like Getter Robo and Gurren Lagann can do the crazy things they do for the same reason that the Hulk can destroy continents just by being angry enough, or a Green Lantern can stitch a planet back together just using willpower and imagination. Gurren Lagann isn't as alien to superhero comic sensibilities is you just think of the green glow that surrounds it when it does its crazier stuff as the same kind of green glow that surrounds a Green Lantern. It is a pretty accurate analogy to what Spiral Power is in Gurren Lagann. The Hulk analogy works too, since the Gurren Lagann does pretty much get stronger the angrier its pilot gets.
As for other examples of really powerful Super Robots, a contender pretty much needs to be able to destroy a planet with one of its lesser attacks. Ideon can slice a planet in half with its Ideon sword, and that is before it breaks out its Black Hole Gun or worse. Shin Getter Robo sliced Jupiter in half with an axe, and that was before it evolved into the much, much more powerful Getter Emperor. I heard that Gunbuster and Diebuster have very infamously powerful mecha. Rah-Xephon is pretty much a god who can control time and remakes reality at the end of its show. As mentioned above, Demonbane is supposed to be ridiculously powerful, but as far as I can tell it is pretty much what would happen if someone turned Cthullu into a giant robot or something like that.
The whole "super robot = god" analogy comes up a lot in the genre, so super robots tend to be fairly powerful, at least in the same sense that the "superhero = god" analogy is common in comic books. Just as Superman is commonly compared to Christ, or Thor is an actual superhero, Mazinger Z is explicitly compared to Zeus within its own mythos.
