A primitive one, seeing as it was Islamic science and work that returned Roman advances to European nations after the Spanish Reconquista. I'm guessing a three way struggle between China, the Persians/Parthians and the Byzantine Empires
I thoroughly disagree - in fact, I consider the spread of Islam as being the latest direct cause of the Dark Ages in Europe, and destruction of coastal Mediterranean civilization at the hands of the Muslims was much to blame for the shift in focus of European development towards the states founded by Germanic tribes, who were far less advanced than the states that existed at the heart of the old Roman world. Also, one has to consider that most of the Islamic scientific advance stopped roughly within a century of the Islamic power being curbed.
Even then, while there were numerous thinkers who did advance science, philosophy, and even technology, when viewed objectively actual overall accomplishments of Islamic science were very often either via translation of earlier antique works, or via transmission of knowledge from the areas the Muslim states had contact with (i.e. the "arabic" numbers, which were an actual Indian invention, etc). In other words, while latter historians blame civilizations like the Byzantines for not advancing the technology much, one has to consider that the much-lauded Islamic civilization was not in any way superior in that regard, and when it got to preservation of knowledge, the Byzantines did the job just as well if not better.
So, on to the original question. I think the world without Islam would not experience Dark Ages as long and, well, dark as our own. There would be a surviving Mediterranean civilization on the northern shore of the Mediterranean, as opposed to surviving only in selected places. While Byzantium's long-term position between Europe, Asia, and Africa might be untenable, the Empire should at the very least be able to maintain its core territories, and remain a serious power for as long, if not longer, than OTL.
Another important effect is that without the need to divert the Imperial forces to keep the Arabs at bay, a full-on Italian reconquest might be possible. It is important primarily due to its effect on curtailing the power of the Papacy early on, thus perhaps leading to decentralization of church power in the Western Europe, where the Byzantines could not effectively reach.
We may not have the glory of the Umayyad Spain, but we will also be spared the Spanish Inquisition (who, ironically enough, learned their lesson from the Almohads and the Marinids quite well, and put it to the same shameful use), the ruin of Italy, and very likely the Crusades, which in turn were retaliation for four centuries of Islamic aggression and ended up being just as violent. Definitely no major Iconoclasm schism here; not quite sure what Persia's future might be ITTL, as after Heraclius it could have possibly recovered in another century or so, unless it were taken over by another power (or a steppe invasion).
Finally, let's think of Africa. Not just of relatively successful Mali, but also of the entire Eastern coast of Africa, and even North Africa, where slave trade prosperred thanks to the direct interference of the Arab raiders and would-be conquerors. Due to the geographical location of the Islamic centers of power, it was one of the possible natural routes of expansion, whereas the early European states had no ability to go there, and the Byzantines had no serious interest in the lands that were not a part of the old Roman territory. Without the disruption brought on by Islam, indigenous sub-Saharan cultures might have had more of a chance to develop, and, better yet, without the buffer of Islamic states around it, Aksum/Ethiopia might actually stand a chance at maintaining serious trade links with Europe, India, China, and developing into an indigenous African power.
All in all, we will end up in a world where OTL's Dark Ages will be merely a century-long interregnum, not a nearly-total collapse of European civilization. To think of what kind of wonders such a world would be able to produce. It would be a "short Dark Ages" TL here, because without the destruction brought forth by Islam, there would be no need to preserve antique knowledge that resulting survivalist cultures did not care for... simply because much of it would not have been destroyed in the first place!