While evidence from the time of the Greeks is spotty, it is thought that Pythagoras and his Pythagoreans may have been rearranging the letters of words in the 6th century B.C., as they believed that anagramming someone's name could reveal information about their destiny. Later, in 332 B.C., Alexander the Great was in the midst of a six-month siege of the city of Tyre, when one night he had a nightmare about a satyr trying to catch him. He asked his soothsayers about it, and they noted that in Greek the word for "satyr" anagrams to "Tyre is thine.". The next day, Alexander finally captured Tyre.
From a very insightful book called The Puzzle Instinct: The Meaning of Puzzles in Human Life by Marcel Danesi:
Soothsayer status was, in fact, often attained by those who claimed to possess knowledge of anagrams. In the third century B.C., for instance, the Greek poet and prophet Lycophron made a profession of devising anagrams of the names of the members of the Hellenistic king Ptolemy II's court in Egypt, as a basis for divining each persons' character and destiny. For this he became widely known and sought out as a soothsayer.After the time of the Romans, there is little evidence of anagram use until its resurgence in the Middle Ages. As most educated people were associated with the Church, most anagrams from that era relate to religion and are in Latin. The most popular example is this imagined exchange between Pontius Pilate and Jesus:
Pilate: Quid est veritas? ("What is truth?")
Jesus: Est vir qui adest. ("It is the man before you.")
I have to admit, it would be really cool to answer somebody with an anagram of their own question.
The Kabbalists were mystics from the Middle Ages for whom anangramming held particular importance. To understand their interest in manipulating letters and numbers, it helps to know a bit about the ancient Hebrew language.
Ancient Hebrew did not have a separate system for numbers, so the letters of the Hebrew alphabet were used instead. This led to numerology (adding up the numerical values of letters in a word, and regarding the sum as significant to the word). Ancient Hebrew also did not have a conventional alphabet; it had an "abjad" which is a writing system where vowels are not written, but inferred by the reader. This made anagramming much easier. (Just imagine how much easier it would be to play Bananagrams if you could use "NRG" for "energy", "GRN" for "green", and "RNG" for "ring"!)
For the Kabbalists, the letters of the Hebrew alphabet held special powers. They developed a wide variety of rule-based systems for transforming one word into another. Some, like Atbash, were simple substitution cyphers (A->Z, B->Y, C->X,...). Temurah (the Hebrew word for "permutation") was the Kabbalistic art of anagramming. The Kabbalists believed that through such manipulation of names and verses in the Torah, they could uncover fundamental knowledge about the universe. They wore anagrams on amulets which they believed protected them from evil (a practice common among many others in the ancient world)
My guess is that if they had had the opportunity to play, the Kabbalists would have been Bananagrams maniacs.
More anagramming history, coming in a future post.