As with just about everything related to the life of the prophet it is completely impossible to say for sure.

The historiography of hadith, tafsir, and the biography of the prophet is a complete rabbit hole from which you can never escape. What your view is on this particular story will almost entirely depend on which of the following views you take on the oral transmission of early Islamic history.

1. Reject all of it as having no reliable basis whatsoever. This is essentially the view of Patricia Crone.
2. Broadly accept the traditional religious views as being the best that we have, while recognizing that some stories are obviously problematic.
3. An intermediate group that accepts a "kernel of truth" model, using a number of criteria to determine which stories are likely to be true. Simple stories are more likely to be true than complex ones. Stories that portray their subjects in a bad light are more likely to be true than ones that portray the subject in a good light. W.M. Watt would be an example of this group (he accepted the story as true.)

The first group would reject this story (edit: actually I phrased this badly, the hadith/sira skeptics wouldn't reject the story, they'd reject the question. i.e. In the absence of documentary or archaeological evidence we can't say anything with any degree of certainty about what happened.) The second could accept it as having been relatively early in its sources or reject it as not having a sound chain of transmission. The third could go either way, with much of the argument coming down to whether or not we are capable of objectively measuring whether the story portrays Mohammed in a positive or negative light, or whether it might not have simply suited the religious/ideological needs of the people who (may have) fabricated it.

Mecca, and the Arab peninsula generally, was a religious melting pot during Mohamed's time. There were various sects of Jews, Christians and other flash-in-the-pan Prophetic/Abrahamic religions which were popular. There were also many old gods and goddesses that were worshiped.

In the Kaaba (the shrine in Mecca where Muslims still make their Hajj) there were shrines to hundreds of different gods when Mohamed was a young man. Mohamed's main religious goal was to eliminate worship of lesser gods and exclusively worship Allah, who was worshiped at the time as the head of the pantheon.

However, (edit. supposedly) in some verses he said that some popular goddesses from the old religion were real, and worthy of worship. This might have been in an effort to make Islam more palatable to conservatives, who generally opposed Islam's radical monotheism. He later (edit. supposedly) claimed that he had been tricked by Satan into reciting these verses and that the arch angel Gabriel later appeared to him and cleared up the confusion.

Since Islam and the Koran are directly based on the sayings/recitations of one man, there are many inconsistencies that seem to stem from Mohamed changing his mind or circumstances changing. The conflicting suras about religious tolerance are another good example of this.

I feel like I should make a general comment about Rushdie that doesn't quite touch on the actual "Satanic Verses", but which is very germane to trying to take historical truth from fiction:

Salman Rushdie is not a historian and his books should not be read as such. He is a novelist, and a extremely poetic novelist at that. He is not trying in the Satanic Verses to give a historical account of early Islam(and the parts dealing with early Islam are a relatively small part of the book anyways); he is trying to articulate something about what it means to be an Indian Muslim with ties to the UK in the latter half of the 20th century and the kind of strange "in-between" experiences it generates. The whole novel is filled strange transformations, unexpected prophets(or madmen) unexpected devils(or saints), and a kind of constant attempting to keep the reader in a state of uncertainty. The parts of the book dealing with the Satanic Verses should be read as part of this, and should be understood as Rushdie taking a historical episode and weaving it into the novel in ways that fits what he is trying to do. This isn't anti-Islamic(although the novel is absolutely full of less-than-veiled satire against Ayatollah Khomeni), it's Rushdie being a novelist, and a very good one at that.

I should also note that this criterion applies to all historical fiction, however well-researched(including for instance History Channel's Vikings miniseries) since by definition literary and narrative considerations are going to be given some priority even when they conflict with actual history. It's just easier to point that out in the case of a novel that begins with two men tumbling out of an exploding airplane reciting a constellation of fragments of Indian and British culture before they miraculously survive their fall to be reborn as a jinn and an angel than it is to point that out in the case of a miniseries done by the History Channel that claims to be a "historical reconstruction", albeit one of dubious value.

I'm kind of surprised, but Wikipedia has a pretty extensive article on the subject. It's not all gold, but the citations are pretty good.

There are fairly early biographies (the first two centuries - by comparison, closer to the source than virtually any known writing on Jesus) that make extensive reference to these verses. The classic version of the story (by Tabari) is that Muhammad was reciting a fairly well-known Sura, but was tempted by Satan to add a couple of lines. Thus, Satanic Verses. Like Buck said, the acceptance of the legitimacy of the verses has been primarily based on how unflattering the verses are. If they weren't real, the earliest scholars should have rejected them out of hand instead of apologizing for them (edit: For clarification, this is not any more preferred a view than any other, and I'd daresay it's not mainstream). Other people have rejected them out of hand - Tabari's early view about their Satanic origin is not accepted by any modern Muslim scholar, as far as I understand, they just dismiss the verses.

Salman Rushdie is referencing real historiography and theology on the idea of these Satanic verses. Their legitimacy is totally unsettled, as per Buck's excellent post.