Myth: Gambit's full name is Remy Etienne leBeau
Truth: Gambit's middle name has never been revealed in the comics. The name Etienne comes from fanfiction, specificially, Lori McDonald's Gestalt Arc. It is hard to convey the popularity of The Gestalt Arc to someone who was not around at the time it was first published. Suffice it to say that more fans were reading that particular fanfiction than were reading the core books, and that it inspired a lot of imitators (including the President of the Guild *coughs*). As a result, many fans started using Etienne as Remy's second name.
If you wish to read the Gestalt arc, it's archived at Fanfiction.net. The simple reason it isn't on LeBeau Library is that Lori wishes to keep it exclusive. We do have many of her other stories, though.
Myth: Gambit has psychic powers
Truth: Gambit's psychic powers are pure speculation on the part of fans trying to explaining his charm power and his resistance to telepathy. There is no canonical evidence to support them.
Myth: Gambit's mother was a prostitute.
Truth: The identity of Gambit's mother has never been revealed in the comics.
Myth: Gambit is the Third Summers' Brother
Truth: This one is complicated!
Most X-Fans believe that the identity of the Third Summers' Brother was addressed in X-Men #39 where it was strongly implied that Adam X or X-Treme was the individual in question. Half-human and half-Shi'ar, Adam was intended to be the son of the Emperor D'Ken and Katherine Summers, conceived when she found herself in his Imperial harem. As such, he would have been the half-brother of Scott and Alex Summers. However, before the plot could be fully resolved, new writers took over the books and it was dropped.
In X-Men: The End, Sinister reveals to Gambit that he created him by fusing his own DNA with Scott Summers' DNA. This would make Remy partially a Summers, if not necessarily a Summers' Brother. However, The End is only a possible future for the X-Men, and therefore it is not considered canonical by most fans.
Ed Brubaker claims that he will resolve this particular mystery in the Dark Genesis LS.
Myth: Gambit was created as a new Longshot
Truth: This rumour started as a result of design similarities between the two characters. They both had similar hairstyles and flashing eyes. There is absolutely nothing in the books to substantiate it. (Although it might explain why Rogue fell in love with Gambit so quickly. She once was Longshot's personal stalker.)
Myth: Gambit was created to be Storm's boyfriend
Truth: In 2003, Chris Claremont stated that Gambit was originally intended to be a villain who would betray Storm and the X-Men, which suggests he was never meant as her boyfriend. In early issues, there were hints about his untrustworthiness, such as Banshee thinking that he asked a lot of questions without giving many answers himself. Similarly, Bishop suspected Gambit of killing the X-Men when he first arrived in the present from his dystopian future.
However, as the character became more popular and Jim Lee and Scott Lobdell took over the writing duties, the original plan for Gambit was dropped. Onslaught became the X-Traitor.
Myth: Gambit usually refers to himself in the third person.
Truth: Only in X-Men: The Animated Series, where he has lines like "Gambit follow you anywhere you go, chere" or "Gambit want to go with ya, Professor." In the comics, he almost never refers to himself as Gambit or Remy in that way, using the first person pronoun like anyone else.
Myth: Gambit only stays with the X-Men because of their money.
Truth: Gambit does not need the X-Men's money. As a world-class thief, he probably has more money than Xavier. During the Assassination Game, he writes a $3,000,000 cheque to Deadpool without blinking. Thinking it is invalid, Deadpool rips it to pieces, only to discover that Gambit could easily afford it.
Myth: Gambit cannot get drunk.
Truth: Another misconception propagated by fanfiction. Certain fans have theorised that Gambit has a faster than usual metabolism, and therefore processes alcohol extremely quickly. There is no real evidence in the comics to suggest that is the case. Gambit speaks about getting drunk on more than one occasion, although he does seem to be joking about it.
Interestingly, Rogue really could not get drunk, as the Kree metabolism she absorbed from Carol Danvers prevented that from taking place.
Myth: Gambit cheats on Rogue the whole time.
In most cases, Gambit's sexual encounters with other women clearly take place before he and Rogue become a serious couple or during various breaks in their relationship.
One exception is Minnie Mastiff, with whom he slept in Gambit #25. However, even there, it seems more likely that he was still broken up with Rogue, given that the last interaction they had in that book was them ending their relationship. Another is Lili Penrose, but, once again, it is unlikely that they did more than kiss.
Because of the ambiguous nature of Marvel's timeline, it's safer to go with what we know about Gambit's character.
1) For Gambit, sex is largely a means of getting affirmation, of knowing that he's loved and wanted. He has that with Rogue already, and he wouldn't risk her love for a one-night stand.
2) Gambit is addicted to stealing rather than sex. That's where he gets his real thrills; that's what really turns him on. Sex is nothing compared to that.
Moreover, Gambit has not been celibate by any definition of the word. Gambit and Rogue were clearly having sex circa Uncanny X-Men #348, Gambit #16, most of X-Treme X-Men, and various other issues where the team lost their powers. He also has had sexual relationships with other women in his and Rogue's many break-ups. Gambit's simply not that sex-starved to have to cheat.
3) It also has been implied that Gambit believes that fidelity is necessary, if he is to redeem himself and create a better life for himself. He doubts whether he is ultimately capable of it, of course, but that's because he doesn't believe he's a good person.
4) Gambit has been shown to find cheating distasteful, probably because he has more respect for his partners than to do that to them. His reaction to Bandit in Gambit #12 clearly shows that he has no liking for cheats.
All of this suggests that Gambit has not cheated on Rogue.