Most fragments of ancient and medieval manuscripts, including representative pages of complete codices, have been digitized.
Papyri holdings may be viewed on Advance Papyrological Information System (APIS): http://www.columbia.edu/cu/lweb/projects/digital/apis/
Medieval manuscripts and fragments may be viewed on the Image Gallery of Digital Collections @ Stanford:
Descriptions accompanying these images are being updated as a long-term project. To request images not already on these sites, or for more information about any of the manuscripts, please write to David Jordan (firstname.lastname@example.org).