The actual "satanic" verses (since no one has mentioned them yet) were not written by Salman Rushdie. In fact they are, according to some sources, from Surah 53:21,22:
19: Have ye thought upon Al-Lat and Al-`Uzza
20: And Manat, the third, the other?
21: Are yours the males and his the females?
22: That indeed be an unfair division!
23: They are but names which ye have named, ye and your fathers, for which Allah hath revealed no warrant. They follow but a guess and that which (they) themselves desire. And now the guidance from their Lord hath come unto them
Source: Marmaduke Pickthall: "The Meaning of the Glorious Koran: An Explanatory Translation"
The "Satanic verses" replace 21 and 22 with the following:
21: These are the exalted cranes (intermediaries)
22: Whose intercession is to be hoped for
Where the cranes represent pagan deities of the pre-Islamic Arabs, namely the three goddesses al-Lat, al-Uzza and Manat, daughters of Allah in the old pagan religion. This would be a concession to idolatry which the same accounts report Muhammad as having made to promote better relations between the early Muslims and the rest of the community who were suspicious of abandoning all their deities in favour of Allah as the only god. Surah 53 is an early one, from before the hijrah and when Muslims were still a minor sect in Makkah. This incident is itself a matter of debate; the majority of Muslim scholars denounce it as a fabrication and many early Islamic writers deny it or don't mention it. Other texts attribute it to Ibn Jarir al-Tabari. On the other hand, there is conjecture stemming from Surah 22:52 that Shaitan had his hand in the revelation of false verses which were later repudiated. 9th century CE scholar Sahih Bukhari is cited as the the source of many controversial reports, though it's not certain where he got the information, and several early (but not contemporary) biographers of Muhammad are also quoted as making references to abrogated verses.
Further, there is at least one account claiming that the Muslims and the pagans prayed together after this revelation. The idea of there either being other gods or of Allah having divine daughters (or, as a matter of fact, Muslims worshipping together with pagans) is unacceptable. 21 and 22 declare it improper for men to believe they have the sons (the prized) and Allah to have only daughters (Islam leaves little room for a dubious concept such as the Christian Trinity that would allow God to be somehow subdivided and compartmentalised). The "satanic" verses are in direct contrast with the Quranic ones. And yes, they conflict with verse 23 which makes them all the more suspect.
Those are the verses deemed heretic and that led to the Ayatollah Khomeini's fatwa declaring the book blasphemous. Though they are not part of the Qu'ran there is a historical record of their existence outside the Qu'ran and they were not invented by a 20th century author bent on offending Muslims.
Addendum (the day after): I'm fully aware that the presentation of this viewpoint (which I myself neither condemn nor condone) may strike some of my Muslim friends as deepest, darkest heresy. Of course I don't quote the entire Surah for context, that's what hardlinks are for... but I added more contextual verses anyway. The English translation at this point is adequate for the explanation (and approved of by prominent scholars of its time); I do not think that this part requires the absolute accuracy of the Arabic text to gain understanding of the point under scrutiny. Please note that this writeup has been elaborated upon and substantially changed from its original form to reflect some valid points made by rk2001. In doing so, I admit that its original form was in need of clarification but also don't care for a confrontational debate.
The book itself is not bad... a decent read but really undeserving of all the attention. Both Gabriel Garcia Marquez and Nikos Kazantzakis did it better.