Another example is the difference in mass between the proton and the neutron, which turns out to be perfect. A difference other than .2% would have resulted only in neutrons, and therefore no protons and no atoms.
Continuing, the amount of matter compared to anti-matter in the first fraction of a second after the Big Bang was such that in spite of massive annihilations the universe ended up matter and not antimatter.
A very good example of a coincidence that is too good to be true, and therefore a candidate for future physics principles, is the fine-structure constant. It has many meanings or definitions; it is known to incredible accuracy; but it remains an enigma to physicists.
According to the highly regarded Richard Feynman, "Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man."