You know, when I first heard of these protests, I was suitably shaken and taken aback. I still am.
But thing is, it's never so simple. Yes, Denmark has free speech. Yes, it had the right to publish that cartoon. But the difference between that cartoon, and the various cartoons mocking Christianity? (Some of which get protested too, by the way...)
As of right now, Islam is being attacked as a religion, and A Big Christian country is doing a rather good job of attacking a large portion of the Middle East. It's also doing a rather good job of demonizing Muslims in general, and marginalizing them whenever it can--or siding with other countries that do so.
The northern European countries are also having, shall we say, some problems with their immigrant populations. It's a rather tense atmospehere, and that cartoon is a rather unwise match in a chamber full of fuel.
Imagine if a paper in America had published a racially offensive cartoon. You can bet there'd be outrage. Hopefully there wouldn't be such violent outrage, but I wouldn't necessarily count on it.