The Moon has huge mountain ranges of comparable height to Earth's tallest peaks. They formed not by tectonic activity, though, but by meteor impacts. Over four billion years of pummeling, mostly on the far side of the moon, have blasted moon rock into piles up to 20,000 feet high tracing the edges of the craters.
Because the Moon lacks an atmosphere, and because its gravity is so weak, these steep mountain piles don't get eroded. Whereas Mount Everest will be gone in a billion years, the Moon's Mons Huygens will hold its shape indefinitely, perturbed only by the occasional impact of meteorites.
In her beautiful essay "You Be the Moon," Amy Leach reminds us: "Nothing makes a sound on the Moon and nothing ever could ... For sound is like birds and cannot travel without air." Just imagine for a moment the completely silent impact of an enormous meteor - the construction of a 20,000-foot mountain without a sound!
Incidentally, in 1934 the philosopher Alfred Ayer used the statement "there are mountains on the farther side of the moon" as an example of a scientific hypothesis that is conceivable and verifiable in theory, but might never be testable in practice.
Only 25 years later, a Soviet probe took pictures of mountains on the far side of the moon that rendered Ayer's statement correct - and his philosophical example obsolete. It is interesting to consider how impossible it seemed in his day to access the moon's dark side, and how soon afterwards we actually did. Perhaps string theorists, multiversers, and the like ought to feel heartened by this... but I'm not sure.