Here's a good thread about this from the FAQ: http://www.reddit.com/r/AskHistorians/comments/sp8dc/would_the_world_be_more_technologically_advanced/

Short answer: No. Christianity helped preserve learning and many universities grew out of church endeavors

No. The middle ages were not "dark" and in fact the university was invented by the medieval Christian church. Science took place at and because of Christian institutions during that time. The cathedral schools, which became universities, were full of scholars trying to learn as much as they could about the world. People were trying their hardest to make progress in every way they knew how, and the church offered a haven for it to happen. The middle ages were a point within a process, not a lost age of darkness. Christianity was not trying to suppress discoveries; it was supporting exploration and learning.

Also, some of the "science" at this time (and later too) was more like what we might call philosophy, occult texts, or just descriptive observation today. There was much discussion about "hot" and "cold" plants and animals, herbal medicine, music coming from outer space, astrology...all this was encouraged and facilitated by the church.

Here is an example of a medieval astronomy treatise (further debunking misconceptions about medieval awareness--as you'll see, they knew the world was spherical): http://www.esotericarchives.com/solomon/sphere.htm#chap2

What we know of as science today was able to blossom because of people's curiosity and the fostering of that curiosity, largely through the medieval university system.

I think it is really important to understand that within the middle ages, a lot of things were discovered, invented, and compiled, which continued in a progression that eventually led to the Renaissance and all the way up until today. People tend to think that it was the dark ages and then suddenly in the Renaissance a bunch of classical knowledge was "discovered" but it's not true. MOST of the sources they had in the Renaissance were the same as in the middle ages, and it's very clear that Renaissance scholars built on the theories of the past and continued to use many medieval ideas and theories (as we still do today). But the people in the Renaissance believed in a new era, and Humanism was an important factor in changing points of view. The people in the Renaissance were still heavily influenced by the middle ages and heavily dependent on the discoveries and theories of the middle ages, as they were, after all, in the midst of the same body of history as ever. But the way people were looking at it started to change, with a greater emphasis on vernacular languages and individualism, as well as a new aristocracy that felt insecure and was trying to find new ways to justify its nobility. Because of all this, people gradually began to build on their past in a different direction, which became the Renaissance. THAT is the biggest defining factor in the new age.

I'm curious about this. Here's a question: Could not Christianities very intolerance of other religions or even variation within it's own, have encouraged some early growth towards scientific thought. For example, in Pierre Chuvin's Chronicle of the Last Pagans he mentions that that in Alexandria the Aristotelian Schools were able to last much longer than the Platonic ones in Athens because it antagonized the Christians less. So if some philosophies, like Neoplatonism were seen as a threat and suppressed, while other more objective ones were viewed less suspiciously, then wouldn't it be easier to proceed in a more objective, "scientific" direction? Wasn't Christianities intolerance of any rival in the sphere of religion encouraging a type of thinking that eventually led to Galileo? That thinkers found in objective reasoning a philosophy that didn't threaten the Church Authorities, well, untill it finally matured? I know there's a big time gap between Justinians Alexandria/Athens and Galileos Italy, but the Church did pretty much maintain the same attitude throughout.