A lot of people hear that glass is a liquid when they hear about this particular misconception. Actually it is probably better to describe glass as an amorphous solid. Any variation in thickness comes strictly from manufacturing processes.
Molten glass is gathered on a blowpipe, and blown to an elongated balloon shape . The ends are cut off and the resulting cylinder is split with shears while still hot, then flattened on an iron plate. This is the forerunner of the Cylinder process. The quality of the glass was not good, with many imperfections.
(By the way, finding original source documents on actual manufacturing of glass is bloody difficult... Many reference pages are dead, and most other pages are referring to this particular "flow" question.)
A bit of history on glass. Humans have known how to make glass starting as early as 3000 BCE (Yale PDF). And the idea of making windows dates back to the height of the ancient Egyptians (though none survive that I am aware of). However, many other glass objects are available for measurement.
The University of California Riverside has a much more in-depth description on their web page concerning the structure of glass, and explaining why it doesn't flow. It concludes with:
There is no clear answer to the question “Is glass solid or liquid?”. In terms of molecular dynamics and thermodynamics it is possible to justify various different views that it is a highly viscous liquid, an amorphous solid, or simply that glass is another state of matter that is neither liquid nor solid. The difference is semantic. In terms of its material properties we can do little better. There is no clear definition of the distinction between solids and highly viscous liquids. All such phases or states of matter are idealisations of real material properties. Nevertheless, from a more common sense point of view, glass should be considered a solid since it is rigid according to everyday experience. The use of the term “supercooled liquid” to describe glass still persists, but is considered by many to be an unfortunate misnomer that should be avoided. In any case, claims that glass panes in old windows have deformed due to glass flow have never been substantiated. Examples of Roman glassware and calculations based on measurements of glass visco-properties indicate that these claims cannot be true. The observed features are more easily explained as a result of the imperfect methods used to make glass window panes before the float glass process was invented.
Glasslinks has some additional information about the properties of glass itself:
“The idea that glass is a fluid is a very widespread myth,” says Yvonne Stokes, a mathematician and spoilsport at the University of Adelaide in Australia. “I was told it as a fact by my adviser. And once, a class of schoolchildren came into the lab, and one of them told me the very same thing. If you want to talk microscopically, then you can call glass a fluid. But people understandably tend to think that if it’s a fluid, it flows. It’s that notion that’s false.”Stokes has recently proved with detailed calculations that old windows could not have flowed perceptibly.
If the myth survives, it will be because it contains a kernel of truth – and because glass is a confusing kind of matter, quite unlike the three ordinary kinds. A gas is an anarchy of molecules going every which way; a liquid is a tighter but still disorderly society in which molecules constantly dissolve and reestablish weak bonds; a solid is a molecular army in rigid formation.But glass is … none of the above. It is rigid like a solid, but its molecules are not arranged in repeating crystals. It is amorphous like a liquid.
In fact, structurally there is no sharp line between a liquid and a glass. You form glass by ‘super cooling” a liquid below its freezing point, then cooling it some more. If you cool it fast enough, the molecules can’t organize themselves into crystals. As the temperature drops, the liquid becomes more viscous and the molecules more sluggish. It’s like a game of molecular musical chairs in which the music never stops and the players never sit down; instead they seem to move through honey, then tar, until they are all but motionless, like bugs in amber.