Intelligent Design? 
ducking and running
If I plug the numbers into Bytegeist’s formula, I calculate that the Sun is 1.8 millirads wide as seen from Jupiter and Callisto is 2.8 millirads wide. So, during an eclipse, Callisto slops over the Sun with about half again as much diameter. Not too bad, but not nearly as snug as the Moon-Sun fit. And certainly, there can never be a Callistan annular eclipse.
If only I didn’t have to work, I’d plug all of the Solar System satellites into a spreadsheet and see if any of them do better. Some of the inner moons of Saturn look promising. Anybody got the time?
That’s hard to say. It depends on the range of distances that could separate the Moon from the Earth. The inner limit would be established by the Roche Limit of the Earth, inside of which the Moon would be torn apart by tidal forces. The outer limit would depend on celestial mechanics–a distant enough Moon would eventually wander off due to perturbation from other bodies. I have no idea what those limits are.
What’s the probability? 1 in 1.
What’s you’re opinion about this “cozy” sun-moon relationship having an influence of the propogation of life on earth. I know it’s a wacky theory, but hear me out. What do you think eclipses looked like during the formation of the earliest multi-celled organisms. Was the moon appearing bigger or smaller at that time? Could the orientation of sun an moon and it’s highly improbable similar ratio of visible light and gravity (and who knows what else) given rise to stable conditions that may have fostered life.
I guess the question I’m asking is–where was the moon when the first blips of life appear on the fossil record?
Yes, that’s the answer. The numbers you cited tell the whole tale. The math is really simple:
The sun’s real diameter is about 403 times the diameter of the moon.
The sun’s average distance from the earth is about 389 times the average distance of the moon from the earth.
Since the one is about 400 times bigger but also 400 times farther away than the other, the match is nearly perfect.
Annular eclipses (where it would be total except that a bright ring of sun appears all the way around the edge of the moon) are explained by the times when the sun is closer and the moon is farther than average.
Math aside, it’s really as simple as Anne Neville suggested. After Orpheus collided with the initial Earth and the impacted material coalesced, it was about 14 times it’s present size. I’m not positive about the timing but have read proposals that dinosaurs hunted under much brighter conditions at night than we now witness due to the much greater reflective surface area present on the moon at that time. It’s since compacted and additionally is moving away from us at the rate of about and inch and a half a year. Eventually it’s gonna be so small as to make your question invalid.
Timing my friend, coincidence based on timing.
The sun and moon won’t be changing appreciable sizes but in time your observed perspective will no longer be similar and, thus, valid.
Here’s a list of apparent angles in milliradians of the sun and moons from certain planets. I got the values from NinePlanets.
Earth:
Sun - 9.29
Moon - 9.05 (Curiously, that implies that most eclipses should be annular, not total.)
Mars:
Sun - 6.10
Phobos - 2.44
Deimos - 0.522
Jupiter:
Sun - 1.79
Io - 8.60
Europa - 4.68
Ganymede - 4.92
Callisto - 2.55
Saturn:
Sun - 0.972
Epimethius - 0.755
Janus - 1.18 (pretty close)
Mimas - 2.11
Enceladus - 2.18
Tethys - 3.59
Dione - 2.97
Rhea - 2.90
Titan - 4.21
Iapetus - 0.410
Uranus:
Sun - 0.484
Cordelia - 0.520 (very close)
Ophelia - 0.593 (pretty close)
Bianca - 0.746
Cressida - 1.06
Desdemona - 0.921
Juliet - 1.31
Portia - 1.67
Rosalind - 0.771
Belinda - 0.907
Puck - 1.79
Miranda - 3.63
Ariel - 6.06
Umbriel - 4.40
Titania - 3.62
Oberon - 2.61
Neptune:
Sun - 0.309
Naiad - 1.21
Thalassa - 1.60
Despina - 2.79
Galatea - 2.55
Larissa - 2.59
Proteus - 3.54
Triton - 7.61
Nereid - 0.0617
Pluto:
Sun - 0.235
Charon - 59.6
So while our moon is the closest in apparent size to the sun, Cordelia is quite close itself, with a couple of others comparable as well. Thus I conclude that it is pretty rare for the moon to be that close in size, but it isn’t extremely rare.
And on rare occasions, a hybrid eclipse where part is annular and part total. There was one such last year in the South Pacific where the first and last parts were annular while the middle was total. At two points during that eclipse, the apparent sizes were exactly the same.
For those not comfortable with milli-radians, Sky & Telescope has these figures in its latest issue:
Moon 29.94 to 33.66 minutes of arc (there are 60 minutes of arc in one degree)
Sun 31.46 to 32.53 minutes of arc
Those are exactly the numbers I was looking for. thanks for finding that. I wish our planet was more special than that, but alas.
Still I wish the Hubble telescope could tell us if other solar systems had similar data.
If we’re able to go there ourselves someday–I hope they address this topic.
Eventually, h*ck, less than 24 hours from now. 
Madrid, Spain around 9 o’clock Greenwich tomorrow, the sun will be visible completely surrounding the moon
As indeed they are. About 60% of all total-or-annular eclipses are annular. If that seems surprising, it’s only because annular eclipses don’t get much publicity because they’re unexciting.
I thought of a simpler way to approach this question. Let’s take it as a given that the Moon is at its current distance, and ask what is the likelihood that it would be sized correctly to fit so snugly over the Sun. Let’s further define a “snug” fit as one close enough so that eclipses can be sometimes total and sometimes annular.
The lower bound on the Moon’s size is obviously something a little greater than zero. For an upper bound, let’s use the size of the Earth itself–if it were bigger, after all, the Moon would be the primary and the Earth the satellite. The Earth is four times the diameter of the Moon, so our range of possible moons would run from 0 to about 120 minutes of arc.
As we have seen, the Sun ranges in apparent size from 31.46 to 32.53 minutes of arc. Because of its elliptical orbit, the Moon will vary from 0.9447 to 1.0585 times its average apparent size. So the minimum possible average size to create a total eclipse, under the most favorable conditions, is 31.46 / 1.0585 = 29.72 minutes of arc. The maximum possible average size to create an annular eclipse under the least favorable conditions is 32.53 / 0.9447 = 34.43 minutes of arc.
In other words, out of a range of 120 minutes worth of possible values, a span of 4.71 minutes, or 4% of the total, produces a fit snug enough to generate a mix of total and annular eclipses.
It makes the coincidence seem a little less amazing.
For eclipses on other planets, remember that you don’t necessarily need to be standing directly under the moon and Sun. They could both be on the horizon, in which case you’d have about a planetary radius more distance from the moon (but no significant change in the distance to the Sun, of course). This would tend to bring Callisto and Cordelia closer to a perfect fit (though I don’t think it would be enough for Callisto, and I’m not sure about Cordelia).
Meanwhile, if the Moon-Sun coincidence has any influence on life on Earth, it’d be due to the tidal effects. The tidal force due to a celestial body is proportional to the body’s density times the cube of its angular size. Currently, the Moon’s angular size is about the same as that of the Sun, and the Moon’s density is about twice as great, so the Moon has about twice the tidal effect on the Earth as does the Sun. I suppose it’s conceivable that there’s some reason it might be advantageous to have comparable tidal effects from two different celestial bodies.
Hasn’t there been some study concluding that on the long term , the Moon has a stabilizing influence on the Earth orbit, hence preventing it from being too erratic over the course of millions of years and making life possible?
I can’t find a cite, but IIRC the theory is that the Moon keeps the obliquity of the ecliptic from shifting chaotically (keeps the Earth tilted at about 23.5 degrees to the plane of its orbit).