The Historia Augusta—one of the major sources for Roman history in the second and third centuries—is written as if it were the collected works of six different historians writing in the time of Diocletian and Constantine. But it’s now generally thought to be, essentially, a work of historical fiction written by a single author about a century later. Nevertheless it’s still an important source, because the forger/author had knowledge of legitimate contemporary sources that have since been lost.

Another example is the works of Pseudo-Dionysius, a fifth or sixth-century writer who claimed be Dionysius the Areopagite (a first-century convert of St. Paul mentioned in the New Testament). The works of Peudo-Dionysius are largely based on the fifth-century Neoplatonic philosopher Proclus, but by connecting it to the Areopagite it was successfully passed off as apostolic Christian doctrine (and accepted as such throughout the Middle Ages).

Greco-Roman antiquity is chocker with texts that came to be misattributed, through a set of processes sometimes called "upward attribution". It can be hard to separate this from "forgery", that is to say, intentional deception. A text might be attributed to a famous author because the real author was unknown; or because it was an imitation of a famous author; or because it came from the "school" of some famous author, and was associated in that way.

One famous example is the famous epigram for the Spartan dead of Thermopylae ("Stranger, go report to the Spartans that here we lie..."), which came to be attributed to Simonides. The play Prometheus Bound is a disputed case. Others include most of the Hesiodic poems; "Xenophon's" Constitution of the Athenians (now better known as the "Old Oligarch"); various philosophical works like "Plato's" Letters, Alcibiades II (and probably I), Theages, and Epinomis, and "Aristotle's" On breath and On virtues and vices; the 13th book of Euclid's Elements; "Apollodoros's" Library; "Hyginus's" Fables; the Culex attributed to Vergil (though that may possibly be authentic); "Seneca's" play Octavia; "Plutarch's" Lives of the ten orators and On music; "Longinos's" On the sublime; and so on, and so on. All of these are certainly false attributions, with the possible exceptions of Prometheus Bound and the Culex. There are many, many others.

Only in a few cases is it really a big deal. The Prometheus is probably the biggest, because it's such a weird play and its dating has a substantial impact on the history of Greek dramaturgy. The seventh of the pseudo-Platonic Letters is also an influential case because of its very direct and lucid treatment of Plato's philosophy.

As a general principle there's no reason to suspect deceptive motives. Each of these texts had a very long history, in which any number of things might have happened to cause confusion in their transmission. In some cases the transmission is a mixture of fact and fiction, like the Journal of "Diktys of Crete", which purports to be by a participant in the Trojan War, and which some few people took as genuine for many centuries.

But the basic problem is that whenever any text is of doubtful authorship, there is a natural inclination towards upward attribution. A famous author adds to the prestige of the text and of the person who's identifying the "author"; but there's very little payoff for caution. End result: over a period of centuries there's a very strong tendency towards misattribution, and no tendency at all the other way.

In any specific case, therefore, it would be prejudicial to assume that a misattribution is a forgery. There may possibly be some cases where the intent was intentionally deceptive -- not including satirical and fictional works, of course -- but I cannot off the top of my head think of any.

(Edit: minor details)

I'm sorry, but we I've had to remove this as it is a Trivia-type question. I would suggest contacting /u/caffarelli however about the topic, as she runs our Tuesday Trivia feature.