Actually, there are a lot of peculiarities to Phobos and Deimos in popular culture.   My argument on Thuria as a hollow world, an O’Neill Colony, is essentially derived from an analysis of Burroughs text, overlaid with modern sensibilities.   But there’s quite a bit of peculiar folklore about Phobos as an artificial little world, that is available for those who go looking for it.

One of these is that the existence of the two Martian moons was actually predicted by Jonathan Swift in Gulliver’s Travels 150 years before astronomers discovered them.   In the section on Laputa, he wrote in unnerving detail of these moons.

http://www.malaspina.org/home.asp?topic=./search/details&lastpage=./search/results&ID=173#lecture

Meanwhile, Phobos and Deimos were deemed to be very peculiar moons indeed.  Their orbits, their sizes and dimensions, their high albedo all prompted one Soviet astrophysicist named Iosef Shklovsky to speculate that the Martian moons might well be artificial structures.  He based this in part, on studies of Phobos orbit which he felt were not sustainable for a natural body.

Among his reasons were, Shklovsky stated Phobos was being "slowed by electromagnetic drag and tidal friction more than was possible was an actual solid moon."   Given that Mars no longer has a live magnetic field, I find myself wondering what ‘electromagnetic drag’ he was talking about.   But you know, that’s Soviet science for you, they couldn’t have known at the time that there was no magnetic field and therefore no electromagnetic drag.  He also based his findings on what was then believed to be the thickness of the Martian atmosphere, which seriously overestimated the actual case.

Now, this finding, sometime in the back in 1958, was no big deal.  The Soviet scientists were always coming up with goofy theories, including the lysenkoist approach to evolution, and the notion that Tungaska was a spaceship explosion.   Soviet science of the 50's and 60's seems to be a wilder and hairier place than the west, largely because Soviet scientists had to spend a lot of time impressing non-scientists in the party establishment, rather than each other.  Thus, a wild and flashy theory would get you further, politically, than a conservative theory supported by proof.

Oddly, Shklovsky found adherents in the west.   In particular, a Dr. Fred Singer, science advisor to President Eisenhower signed on in 1960, supporting the Shklovsky theory.

Now, I’m not sure what Singer’s field of specialty was.   But judging from this corker, from Singer about Phobos “its purpose would probably be to sweep up radiation in the Mars' atmosphere, so that Martians could safely operate around their planet.” I wouldn’t put too much faith in the guy.  His conception of a cosmic hoover, while pictaresque, is staggeringly illiterate.

Astonishingly, a few years later, in 1963, Raymond H. Wilson Jr., Chief of Applied Mathematics at NASA, climbed on board, stating that "Phobos might be a colossal base orbiting Mars." He also stated that NASA itself was considering the possibility.

http://www.rense.com/general20/eisenhowerWH.htm

Now the case for Phobos, based on 'impossible orbital eccentricities' which suggested that it was a hollow body rather than a solid one, seems to be one of those conclusive things.   A hollow body would mass much less than a solid one, and its mass would be distributed differently.   

You could then dope this out by carefully studying the orbital permutations.  As pure mathematics, it would admit to no errors.   The face on Mars may be subjective, but the structure of Phobos orbit is not.

Nevertheless, the subject faded away.  I can’t find any further serious or semi-serious references to possible artificiality of Phobos based on orbital mechanics after 1967-69.   Which, coincidentally, would be about the same time that Russian and American space probes were arriving which would have gotten the most accurate readouts on Martian conditions, and the best data on orbits yet.

So, my assumption is that the orbit hypothesis simply evaporated.   The data was refined, the mathematics were double checked, and voila, it turned out that there wasn’t anything patently artificial in Phobos orbit at all.

Meanwhile, a few years later, as pictures from space probes began to come in, it became clear that Phobos was a lot weirder looking than anyone had imagined.   For one thing, there was an immense deep crater in one side of the moon, something that might have looked suspiciously like an airlock.   For another, there was a series of reasonably straight, reasonably parallel lines or grooves streaking across the surface.

Unfortunately, these images came out at an inopportune time.   Well after the death of Shklovsky’s hollow satellite theory, and well before the Cydonia theories.   So, for the most part, Phobos remarkable features were considered ‘remarkable’ and nothing more.

Still, if we take a look at it, it’s quite visually arresting.

http://news.bbc.co.uk/1/hi/sci/tech/4004001.stm
http://space.about.com/library/weekly/bliphobos3.htm

Just for the record, here's one of Deimos.

Of course, it was inevitable that Phobos would get swept up in the Cydonia theories, particularly as those theories lost any basis in reality and became outright projection fantasies.   Here are a few cute links.

Strange Moons of Mars
Soviet probe meets ufo on Phobos mission?
Chain Craters of Phobos
Cydonian Imperative
Mars Anomalies
UFO Area Phobos
Astronaut "UFO" Sightings The favourite loony theory appears to be that there was a possible spaceship or foreign object hanging around Phobos that destroyed one of Earth’s space probes.   This is less Cydonia, and much more conspiracy theory.  But it all intersects.  Other researchers have concentrated on peculiar ‘crater chains’ or anomalous boulders.

Carlotto's animation shows the Face as seen from the direction of the "City" based on Viking and MGS data.