The age-old question of Canon is one of the most salient points of the debate, and has perhaps substituted the actual technical debates as the key issue in the whole Star Wars vs. Star Trek argument.
What is canon?
Simply put, canon is what is considered to be reality in any given sci-fi universe. The difference between canon and non-canon material is that any new material intended to be canon must respect and not contradict any previous canon materials. Of course this doesn't always happen in reality, but that's how it's intended to work.
Star Wars canon
There are four main levels of canon within the Star Wars universe, which work together to create what is known as the overall continuity of the Star Wars universe.
- G-Canon: This consists of the six Star Wars films, and adaptations of them such as novelizations and comics. Nothing is permitted to contradict these in any way, at least not while remaining in the overall continuity.
- C-Canon: The vast majority of Star Wars material, such as novels, short story collections, comics and selected video games. C-Canon material cannot contradict G-Canon material, but it is quite possible for the reverse to happen. In practice though, this is not likely to happen in the future, unless the proposed Star Wars TV series is designated canon. The Incredible Cross-Sections book falls into this category, which helped spark the whole continuity debate in the first place.
- S-Canon: Usually made up of older or less serious material. S-Canon material still counts in the overall continuity, so long as it is not contradicted by anything at the G or C levels.
- N-Canon: Material in this category is not part of the Star Wars continuity, either because it has been contradicted by the films, or because it was meant to take place in an alternate timeline, for instance. There's some debate about whether the original, pre-Special Edition films belong here; some say that Lucasfilm has decanonized the originals by withdrawing them from distribution (though they've since made them available on DVD again). On the other hand, there are also those who argue that both are equally valid versions, or even that the Special Editions are in fact the N-Canon versions, as they are obviously edited versions of the originals.
A rigorous checking process is employed to ensure that all new C-Canon material is in compliance with other G and C-Canon material (keeping continuity with S-Canon is less important). In some cases, works have been delayed while continuity problems are sorted out. This, and the fact that there is a specific category for non-canon material, shows that Lucasfilm and its subsidiaries consider most of their material to be part of an interlocking canon, which they try (if not always succeeding) to preserve.
Star Trek canon
The creator of Star Trek, Gene Roddenberry once said that "It isn't Star Trek until I say it's Star Trek." This statement generally isn't taken seriously however, as it would render all material made since late 1991 non-canon. In practice, all on-screen material from the ten films and five television series is considered to be canon (Star Trek: The Animated Series isn't normally considered canon, but generally isn't contradicted by the following films and series, either). The impending eleventh film might further complicate matters, but this is how it stands for the time being.
Star Trek also has its own novel series. The rules for this are defined by the Pocket Books (the arm of Paramount in charge of the novels) submission guide, which states that continuity with the films and shows must always be respected, and while contradicting other novels is discouraged, it's not actually forbidden. This in effect means that Star Trek is divided into two canon levels, roughly equivalent to the G-Level and N-Levels of Star Wars.
Some confusion was raised when Star Trek: Voyager producer Jeri Taylor wrote two novels (Mosaic and Pathways) and declared them to be canon. This was mainly for the purposes of providing background for Captain Janeway; the details in the book were not picked up on by other writers however, and parts of the book were later contradicted outright on the show, firmly establishing the book as non-canon, an establishment strengthened when a statement was released reinforcing the fact that all the Star Trek books are effectively non-canon.
The Canon Debate
Despite both Lucasfilm and Paramount making relatively clear statements on the canon and continuity of their respective series', some have chosen to argue against these positions. The most common claim is that no Star Wars material other than the films is canon, and this is usually "supported" by a quote by George Lucas, saying that the films are supposedly in a "parallel universe" and "don't intrude on the films, but intrude between them." While this is generally understood as meaning that the novels and other official materials are not allowed to contradict the films but are otherwise entirely valid, some have chosen to interpret Lucas' statements as meaning that the novels take place in a separate reality, and therefore (for some reason) have no validity.
There are also those who try and claim that the Star Trek novels are canon, but this position is much rarer, as the Trek novels being canon would not greatly benefit the overall chances of the Star Trek side.