The BBC News website looks at why the depictions have caused such offence.
What does the Koran, the holy book of Islam, say on the issue?
There is no specific, or explicit ban on images of Allah or the Prophet Muhammad – be they carved, painted or drawn.
However, chapter 42, verse 11 of the Koran does say: “[Allah is] the originator of the heavens and the earth… [there is] nothing like a likeness of Him.”
This is taken by Muslims to mean that Allah cannot be captured in an image by human hand, such is his beauty and grandeur. To attempt such a thing is seen as an insult to Allah.
The same is believed to apply to Muhammad.
Chapter 21, verses 52-54 of the Koran read: “[Abraham] said to his father and his people: ‘What are these images to whose worship you cleave?’ They said: ‘We found our fathers worshipping them.’ He said: ‘Certainly you have been, you and your fathers, in manifest error.'”
From this arises the Muslim belief that images can give rise to idolatry – that is to say an image, rather than the divine being it symbolises, can become the object of worship and veneration.
What does Islamic tradition say on the matter?
Islamic tradition or Hadith, the stories of the words and actions of Muhammad and his Companions, explicitly prohibits images of Allah, Muhammad and all the major prophets of the Christian and Jewish traditions.
More widely, Islamic tradition has discouraged the figurative depiction of living creatures, especially human beings. Islamic art has therefore tended to be abstract or decorative.
Why is the insult so deeply felt by some Muslims?
Of course, there is the prohibition on images of Muhammad.
But one cartoon, showing the Prophet wearing a turban shaped as a bomb with a burning fuse, extends the caricature of Muslims as terrorists to Muhammad.
In this image, Muslims see a depiction of Islam, its prophet and Muslims in general as terrorists.
This will certainly play into a widespread perception among Muslims across the world that many in the West harbour a hostility towards – or fear of – Islam and Muslims.