How rare are earth-like solar eclipses? Solar eclipses on the earth are so spectacular because the moon has roughly the same size as the sun when viewed from the earth's surface. This is an incredible coincidence, and my guess is that it is a very uncommon phenomenon in the universe.

Is it possible to say anything sensible about the likelihood of a planet having a moon and a sun with same apparent size? Is it possible to make an educated guess about how many places in the universe you would be able to see an earth-like solar eclipse?
We can certainly speculate.

There are dozens of moons in our own Solar System. I've done some preliminary calculations of their apparent size as seen from the planet vs. the apparent size of the Sun at that distance. The large moons (Jupiter's 4 Galilean satellites, Saturn's Titan, Neptune's Triton) are all substantially larger in the sky than the Sun is. I think there are some satellites that are fairly close to the apparent size of the Sun, but I haven't done all the calculations.

The apparent size of our Moon has changed over time, as the Moon has gradually moved farther away. We are coincidentally in a period of history in which it happens to be very nearly the same apparent size as the Sun.

The criterion for an exoplanet to have solar eclipses like the spectacular ones we have here on Earth is a moon that happens to have an angular size large enough to cover the photosphere, but not so large that it also hides the corona.  For a larger moon, you'd have eclipses in which the corona is visible, but not all the way around the moon. For a smaller moon, you'd only have annular eclipses.  (It could also get interesting if you consider eclipses as seen from other moons.)

So given the distribution of sizes and distances of moons in our Solar System, we can guess that situations where the apparent size of a moon and sun closely match is fairly rare, but since there are moons whose apparent size is smaller than the Sun and others whose apparent size is larger than the Sun, it probably happens sometimes.

The one piece of the puzzle that we're still missing, I think, is the typical sizes and distances of satellites of Earth-like planets. Moons the size of ours orbiting habitable planets might be common or very rare. If they're rare (say, if Mars-like moon systems are far more common), then Earth/Moon style eclipses might be very rare for habitable planets.