Well, I'm not going to let other people put words in my mouth. As a Muslim, I'll tell you what I believe and hear Islam teaches us on this matter.
Muslims love the Prophet Muhammad, peace be upon him, and even love him more than their families. That may surprise some, but it is part of the religion; many ask God to bless him after every prayer. It's no surprise that people get offended when people accuse him of being a violent person, when that wasn't the case. However, it doesn't get violent usually.
This effrontery has happened in the past; when Jerry Falwell went on international TV calling the Prophet Muhammad (pbuh) a "terrorist", and there was plenty of international anger enough to force him to apologize, but there wasn't rioting or destruction. That issue didn't have political meanings and undertones the way this current train wreck is. When the Quran was flushed at Guantanamo, there were demonstrations, but only a little violence erupted in Afghanistan, where there was discontent with the US-backed leadership.
As Muslims, we know that the Prophet Muhammad was subject to ridicule, insults, and attacks on him and his people. He had to endure years of suffering at the hands of the polytheists in Mecca, who tortured and killed his companions, tried to starve him, sabotaged him, and denied him rights given to all members of his society. However, he dealt with it all patiently and never sank to their level, and I give him so much respect for this.
Muhammad (pbuh) once went to the city of Ta'if to tell them about God, and they pelted him with stones so badly that he was covered in blood and his shoes filled with it. God sent an angel, some say it was Gabriel (peace be upon him), who offered Muhammad (pbuh) a choice to have the people destroyed and the city crushed by angels (like Sodom and Gomorrah). He refused and said no, perhaps one day their descendants will become Muslim. Were he alive today, I believe he'd shrug the cartoons off.
Muslims aren't allowed to insult other religions, as people from other religions will insult us back. Besides, God has our back.
While the Prophet Muhammad (pbuh) was sitting with some of his companions, a man insulted one of them. The person who was insulted remained silent. He was again insulted, but controlled himself. He was insulted a third time, and then he retaliated. At that point, the Prophet got up to leave. The man who was insulted said: "Are you angry with me?" The Prophet replied, "While you were not reacting to the insults an angel came down from Heaven and was rejecting what had said against you [by yelling back at him on your behalf] . But when you retaliated, a devil came down. I was not going to sit when the devil came down."
There's a story of a woman who would yell and spit at the Prophet Muhammad (pbuh) and throw dirt at him every time he walked to the mosque. He never did anything back, just ignored it. One day, she was absent from this routine, not at the door yelling at him like she did every day. He found out that she was sick and he went to visit and took care of her instead. Yes, to the very woman who threw dirt at him.
"Believers, let no man among you mock another man; the man being mocked is usually superior to the man who mocks. Let no woman among you mock another woman; the woman being mocked is usually superior to the woman who mocks. Do not slander one another, nor call each other by rude names; it is wrong that someone who has embraced the faith, should be called by a rude name. Those who do not repent, are sinners." Qur'an, Al-Hujurat, Surah 49:11
What do I feel as a Muslim? I want this all to go away. From a religious aspect, we're not supposed to insult the Danes' religion back, and we couldn't either; as Jesus, peace be upon him, is a revered prophet and messenger in Islam. Attacking, or threatening to attack Danish and Norwegian people indiscriminately is also wrong. I condemn the cartoons, and the resulting violence. It's just counterproductive to the cause.
From a political aspect, I'm sick of the double-standard. Europe has anti-Semitism laws that restrict certain hate speech. However, those laws are applied unequally; holocaust-denier David Irving is in jail for anti-Semitism charges, but Islamophobic stuff gets printed and spread legally. You can't watch Al-Manar TV in Europe, but you can call for the expulsion of all Muslims from Europe, as right-wing groups like the National Front have. A political cartoon in the UK of Ariel Sharon eating babies got formal protests and legal threats from a bunch of European governments, but the Danish PM refused to meet with several Arab ambassadors when these much more insulting anti-Islam cartoons got printed. Europe criticizes Arabic newspapers for anti-Semitic content, but gets all defensive when Arabs criticize European newspapers for Islamophobic content. Also, this issue also had anti-immigrant undertones, which are an ongoing problem in Europe. There's other issues from last year; why is a nun respected for wearing a habit, but when a Muslim woman puts a headscarf on, Europeans call her "oppressed?" See why some people got so upset?
Someone is Insane in the State of Denmark.
Slate.com: What to Arab Journalists think of the cartoon scandal? also blogger and professor As'ad AbuKhalil weighs in on the hypocrisy