I've seen that in games where a player has an "arsenal" of several characters and each time he plays with one of them, like MMORPGs and the Diablo series, people refer to their characters as "toons". What is the source for this term?
Much of this is my opinion and recollection, but as a gamer for 25 years (MMO-gamer since Everquest) maybe I know a thing or two.
Character vs Toon
"Character" is the word old RPG players have used to describe their avatar. MOO's, MUD's, D&D, Champions, and many other pen-and-paper systems. Role-playing has an important concept of separation of "player knowledge" and "character knowledge" - what you know vs what your character should know.
Many RPG players cringe when the word "Toon" is used to mean "character". "My character" implies a connection with my identity (or at least something my identity participates in), while "my toon" is something possessed, disconnected from me. More on that later.
Pre-MMO History of Toon
While these examples don't authoritatively show the origin of the word Toon, they do establish that the word was in use prior to the existence of MMORPGs.
How did Toon come to be used to describe characters?
While ToonTown's characters are, in fact, toons, the term has been used in earlier games. My recollection is that the term mainly was used in out-of-game character/account real-money trades. The word "Toon" provides a solid disconnection between the player and what he made, allowing him to sell it without regret.
Also, consider the character systems of Diablo 1 and 2. You pick your class and then the character's appearance and gender are determined from that. If you are a male gamer playing an Amazon or a Sorceress, calling that character a "Toon" can be a signal to others that you don't identify as that gender. Once again, there is a separation from identity.
Still, these games all pre-date the rise of the term around 2006. I attribute the rise of the term "Toon" during this period as not belonging to a single game or experience, but instead to the increasing disconnection between player and character identity. This can be due to many MMO players playing second or third games - how many character connections can a player create or sustain?
This can be due to games becoming more action-oriented (vs role-play centred), there is more focus on what actions this mechanism or "Toon" is capable of, instead of what the character would do/say/feel.
The Realm Online
This game was released by Sierra in 1996. It features animated cartoon-like characters. The oldest usage of "Toon" I have identified so far comes from this game (see reference below). Because the game lacked a two-way trade system, scamming was a common occurrence. It seems reasonable to me that the characters created for the sole purpose of scamming would not be called "character", but would instead be labeled "toon".
References (more to come as I have time):
It goes back to the movie "Who Framed Roger Rabbit", released in 1988. Check the IMDB listing first sentence: http://www.imdb.com/title/tt0096438/?ref_=fn_al_tt_1