EDIT: 40 million pages, not documents. Phase 1 of that project is 3000 manuscripts.
Confining myself to documents with some form of writing or proto-writing on them beyond numerical calculation, here are some Uruk IV texts, from the one of the oldest levels of Uruk and among our most important witnesses to archaic Cuneiform, now in the Vorderasiatiches Museum, Berlin:
Here is a somewhat later group of Archaic Cuneiform texts from the same period from a range of sites, now in the Oriental Institute in Chicago: http://cdli.ucla.edu/search/search_results.php?SearchMode=Text&Collection=oriental+institute&Period=uruk+i&requestFrom=Search
The exact dating of these texts is uncertain because they come from secondary archaeological contexts, but they probably date to 3500-3200 BCE.
Cuneiform studies has generally been extremely active in digitization efforts. The Cuneiform Digital Library Initiative (http://www.cdli.ucla.edu/) is an enormous project to photograph and put online a massive range of cuneiform texts from all periods in all the major tablet and artifact collections. In many cases, these have been transcribed and a few are even translated. Beyond the CDLI's work, a wide range of databases have sprung up to provide copies, transliterations, and translations of texts ranging from Sumerian royal inscriptions to Neo-Assyrian diplomatic correspondence for more specialized purposes. Many of these databases can be found through http://oracc.museum.upenn.edu/.
Well, there are photos of the Kish tablet online, which is the oldest written document ever discovered
41 million documents
From the original press release:
The project consists of an initial four-year phase during which three thousand manuscripts will be digitised, which may be extended into a second phase to include the 82,000 volumes – more than 40 million pages – of manuscripts preserved in the Library and dating from between the second and twentieth centuries.
If I may build on this... What's the oldest one in English?
When I studied Greek at a uni in central Texas, we were one of three schools to be granted a facsimile text of the Codex Sinaiticus.
Sure there are older texts online, but this is one of the oldest Biblical texts, and oldest complete copy of the New Testament. It was handwritten over 1600 years ago, and is also the oldest substantial book to survive antiquity, and the full text is available online..
For those that have a few years studying classical Greek, it is really a treat. There are no spaces in between the words, because as it was being handwritten, the scribe(s) wanted to conserve the paper material they used, and ink.