A great online resource for medieval manuscripts is the Digital Scriptorium, now based at Columbia University. This very comprehensive site now includes manuscripts from Columbia, Harvard, the New York Public Library, the Library of Congress, the University of Pennsylvania, Yale University, and other libraries. Manuscripts from the Free Library of Philadelphia will be available at the Digital Scriptorium in the future. The Scriptorium has detailed descriptions and images of thousands of manuscripts, and more are being added all the time. For the study of manuscripts across many different repositories, this is an essential resource.
One of the very finest collections of manuscripts in the world is located at the Pierpont Morgan Library & Museum. You can also search the Morgan's "Corsair" catalog for full descriptions of bibles, Books of Hours, and other manuscript genres.
Many libraries around the world with manuscript collections have developed their own digital catalogs. One of the greatest collections, assembled over many centuries, is at the British Library. The catalog is easy to search and has very good images.
You can also view about 1,000 images from the fine collection at the University of Oxford's Bodleian Library.
Not a scholarly catalog, but a wonderful gathering of images from manuscripts in French collections can be found at Enluminures. Images are arranged thematically, so you can view many scenes of knightly combat, Nativities, etc., in very good digital images. Please note that the text is in French only.
In 2001, an exhibition of illuminated manuscripts titled "Leaves of Gold: Illuminated Manuscripts from Philadelphia Collections" appeared at the Philadelphia Museum of Art. The online version of the exhibition has many beautiful manuscripts, as well as useful explanatory material on how manuscripts were made and used.
The Labyrinth site at Georgetown University has a rich selection of Latin texts and other resources for medieval studies.