this article, I found out that the Vatican Library is uploading many of their manuscripts and books, and are putting them online for us all to see!
Of course, this is a project that will take time to finish, and as of the writing of this post, they have only done 4,200 or so of their 82,000 documents, but still, that's a lot of manuscripts to go for for gaming inspiration and handouts. Even if most of them are in Italian or Latin, some of the illuminations alone are worth the effort of digging through. Which does raise one issue, the means for searching through the documents leaves a lot to be desired.
The other issue is of course the surroundings are nowhere near the same as if you were in the actual Vatican Library, but a google image search will soon fix that.
Also, there's no mention of when they're going to get round to their secret archives, as lets be honest, that's what we're really all interested in!