Actually, there is an obvious answer to this obvious question, and it's one that knee-jerk defenders of free speech (such as me) should understand. It is that the drawings really are seriously offensive to some people. The cartoons occur in an overlap area, in that they are instances both of a traditional class of protected speech (political speech, expressions of ideas) and a traditional category of behavior that is not protected: conduct that is offensive to others.
As to the latter category, even John Stuart Mill, the great defender of free speech, said:
Again, there are many acts which, being directly injurious only to the agents themselves, ought not to be legally interdicted, but which, if done publicly, are a violation of good manners, and coming thus within the category of offences against others, may rightfully be prohibited. Of this kind are offences against decency....
Since Mill mentions "offences against decency," it's natural to think that the offense against others that he is talking about here is simply the emotional offendedness that people experience at the site of, say, public nudity. But then, if such emotions justify legal coercion, what happens to free speech? The sorts of ideas that we are actually tempted censor are always ones that are offensive to someone -- that's why we censor them! That's the whole problem with those cartoons. Where do you draw the line?
I think there is a line that a follower of Mill (note: this doesn't include me -- Mill's defense of liberty is too weak-kneed and flexible for me) might draw. You could say that your offended feelings don't count as a basis for coercion if the feelings are based on moral, political, or religious disapproval. If I publish a drawing making fun of your prophet, you will be offended because you disapprove of the drawings. If you censor the drawings, you are merely enforcing your religious opinions.
On the other hand, if I build a pig farm next door to your house, and you find the smell offensive, the reason you are offended is not that you morally, politically, or religiously disapprove of pigs or pig dung. If you sue me, you are not enforcing your Weltanschauung, but merely defending your rights.
The line to draw separates offense that is based on normative opinions and offense that seems to be hard-wired in the human brain. The Muslims who demand that those who publish the cartoons be punished are sincerely offended, and that is unfortunate, but it is also true that they are on the wrong side of this line. They are trying to ram their view of the world down other people's throats.