First before anything else we need to know why even bother with canon. The answer is simple because with out it we wouldn't know what can and can't be used when analysing Sci-Fi. In short canon is what is "true" or what really happened from a historical perspective in each series. Without knowing what is true and what isn't we can't analyse sci-fi.

Star Trek Canon

What is Paramount's canon policy for Star Trek? The FAQ on the official web site makes things quite clear.

07.10.2003

"How do the Star Trek novels and comic books fit into the Star Trek universe? What is considered Star Trek "canon"?

As a rule of thumb, the events that take place within the live action episodes and movies are canon, or official Star Trek facts. Story lines, characters, events, stardates, etc. that take place within the fictional novels, the Animated Adventures , and the various comic lines are not canon.
There are only a couple of exceptions to this rule: the Jeri Taylor penned novels "Mosaic" and "Pathways." Many of the events in these two novels feature background details of the main Star Trek: Voyager characters. (Note: There are a few details from an episode of the Animated Adventures that have entered into the Star Trek canon. The episode "Yesteryear ," written by D.C. Fontana , features some biographical background on Spock .)"

-Star Trek.com, Official FAQ,07.10.2003

As you can see Star Trek canon policy is quite clear. All five live action shows and all ten movies are canon, as well as "Mosaic" and "Pathways".

Star Wars Canon

Star Wars canon isn't as simple as Star Trek canon because there are multiple, contradictory statements about canon from various people at Lucas Film Limited. Lucas Licencing and Lucas himself.

Lucas quotes:

"There are two worlds here," explained Lucas. "There’s my world, which is the movies, and there’s this other world that has been created, which I say is the parallel universe – the licensing world of the books, games and comic books. They don’t intrude on my world, which is a select period of time, [but] they do intrude in between the movies. I don’t get too involved in the parallel universe."

-George Lucas, July 2002 - as reported on the Cinescape site, from Cinescape Magazine

As you can see Lucas considers the Expanded Universe (EU) to be a separate and parallel universe from his own.

"STARLOG: The Star Wars Universe is so large and diverse. Do you ever find yourself confused by the subsidiary material that's in the novels, comics, and other offshoots?
LUCAS: I don't read that stuff. I haven't read any of the novels. I don't know anything about that world. That's a different world than my world. But I do try to keep it consistent. The way I do it now is they have a Star Wars Encyclopaedia. So if I come up with a name or something else, I look it up and see if it has already been used. When I said [other people] could make their own Star Wars stories, we decided that, like Star Trek, we would have two universes: My universe and then this other one. They try to make their universe as consistent with mine as possible, but obviously they get enthusiastic and want to go off in other directions."

- George Lucas, Aug. 2005 - "New Hopes" interview in Starlog #337

Once again Lucas states that the EU is separate from the His universe (the movies and to a lesser extent the novelizations of those movies). Note how Lucas says Star Wars canon is like Star Trek canon, in other words the live action movies/TV is canon and the rest isn't. Therefore according to Lucas: Movies = Canon, EU = Parallel universe

Lucas Licencing quotes:

"Gospel, or canon as we refer to it, includes the screenplays, the films, the radio dramas and the novelizations. These works spin out of George Lucas' original stories, the rest are written by other writers. However, between us, we've read everything, and much of it is taken into account in the overall continuity. The entire catalog of published works comprises a vast history -- with many off-shoots, variations and tangents -- like any other well-developed mythology."

-Star Wars Insider #1

According to this quote the novels, the radio dramas and the screenplays are all canon as well (though at a lesser extent than the films) because they are direct spin outs of the movies, so far no problems. The next part of the quote is a little more problematic because according to this quote everything (EU) is part of a larger overall canon that is contradictory to George Lucas' statements.

"Just what is Star Wars canon, and what is not? The one sure answer: The Star Wars Trilogy Special Edition- the three films themselves as executive-produced, and in the case of Star Wars written and directed, by George Lucas, are canon. Coming in a close second we have the authorized adaptations of the films: the novels, radio dramas, and comics. After that, almost everything falls into a category of "quasi-canon"."

-Star Wars encyclopaedia

Once again we have a clear quote saying that every thing other than the movies, novelizations, screenplays and the radio dramas are non canon. It should be noted that the DVDs replaced the SE films and therefore the SE are canon no more and the DVDs are (more information in latter update). But also according to this quote everything else falls under a "quasi-canon" (i.e. canon unless contradicted).

Putting it all together:

Now we have several contradictory quotes (note that there are many more quotes out there but I chose these because the represented the general content of the vast majority of the other quotes out there) that say the EU is either canon or non-canon, so what are we to do? The answer is obvious, who has the most authority over Star Wars? George Lucas of course. So therefore when faced with a contradiction we should take Lucas' statements over that of other people.

Conclusion