I never liked the manhole cover question because most people really don't like it when you tell them that the answer they have is wrong. It's not entirely because they don't fall in the hole, that's part of it, but it's also because of the two shapes that satisfy that requirement they are far easier to manufacture.
The second shape is an equilateral triangle and they have been used in the past for manhole covers, most notably in New Hampshire. They're falling out of use because of the fact that circular ones really are that much easier to manufacture and have a few other advantages such as the fact that they have no tips to break off (though to be honest I don't know how easy it is to break the point off a triangular manhole cover).
Manhole covers are round because manholes are round. The question is why manholes are round?
Manholes are round because round shaft requires less material for the walls to hold soil pressure. The same reason why most wells are round. As a matter of fact when this is not a concern manholes and their covers quite often are not round - just walk on the sidewalk in any modern city.
You can walk quite a way in Britain before you see a circular manhole cover. Domestic drain covers are almost always rectangular galvanized steel, and aren't actually that heavy, so dropping one doesn't happen that often.
Digging and constructing a rectangular inspection pit is much easier than a circular one.
There isn't a wrong answer to this question unless you are asking an engineer about a specific manhole cover they have data about.
> Manhole covers are round because manholes are round.
That's clearly not the whole story. There is no reason why a shaft has to be covered by the same shape as the shaft. If there were significant drawbacks to having round manhole covers, we'd just have another shape with dimensions large enough to not fall down. There aren't, in fact round covers are fairly easy to manufacture as long as high precision isn't required, as simcop2387 noted.
There is a strong reason for the shaft to be covered by the cover of the same shape: it requires less material than any other shape. So with all else being equal, it's the optimal shape; it makes sense to use other shape only if there are other outweighing concerns.
The second shape is an equilateral triangle and they have been used in the past for manhole covers, most notably in New Hampshire. They're falling out of use because of the fact that circular ones really are that much easier to manufacture and have a few other advantages such as the fact that they have no tips to break off (though to be honest I don't know how easy it is to break the point off a triangular manhole cover).