Bodleian Library (Oxford University): main site; MS images selection. Based on the collection of Duke Humphrey, duke of Gloucester, with additions from other early book collections and from being named a "legal deposit library" for newly printed books in the United Kingdom (corresponding to our Library of Congress).
British Library Manuscript Collections: The largest single collection of English language MSS in the world, the British Library MS Collections offer some nice digitization projects as well as a robust search engine linked to a superb descriptive catalog.
CEST: Codices Electronici Sangallenses: The library of St. Gall (Switzerland) has been in existence in one form or another for over a thousand years. It is the only surviving monastic library in the world. This project makes available high-quality digital images of the MSS to enable scholars to study their texts and illuminations without stressing the originals. The collection can be searched by author, title, age, language (but it's almost all Latin and varieties of German), and signature (i.e., so that you can see first/last signatures to compare bindings). You also can search (from the right pane) from the bibliographic description of the contents to the images of the pages containing them. Remember that Medieval MSS almost always tend to contain numerous works, not just one, often in different languages, hands, etc.
CEEC: Codices Electronici Ecclesiae Coloniensis: Manuscripts from the Cathedral Library of Cologne, digitized in an earlier initiative like that which produced the St. Gall MS project, above. To get to the limited English-language support, click the "Optionen" tab on the upper right of the home page and select "English." Let the site teach you a little German and you will be able to navigate it with relatively little difficulty.
CORSAIR: The Morgan Library (NYC) image bank of digital surrogates taken from their collection of Medieval and Renaissance manuscripts.
Library of Congress Digitized Materials from the Rare Books and Special Collections Division: The crown jewel of the LOC collections is the Lessing J. Rosenwald Collection of manuscripts and rare books. Other collections of Americana are important to the study of colonial and early Republic history.
Textmanuscripts.com: Not an "archive" as we understand it, but rather a commercial dealer in early manuscript books. The site offers the browser a chance to see digital images and careful bibliographic descriptions of many manuscript and early printed books.
Bibliotheque Nationale Francais, " The Age of King Charles V (1338-1380)": The French king whose reign overlaps that of the English William III and Richard II (Chaucer's youth [c.1340-1499]). The digitized MSS include four different MSS of Froissart's Chronicles (C15), a C14 Chronicle of France, The Catalan Atlas (C14), Bartholomeus Anglicus' On the Properties of Things in two MSS (C15), John of Berry's Petites Heures (C14 cousin of the Tres Riches Heures), Gaston Phoebus' Book of the Hunt (C15), and the Breviary of Martin of Aragon (C15).
CHD Center for Håndskriftstudier i Danmark, Dismembered Manuscripts: Again, not an "archive" as we understand it, but an online project reclaiming digital images of Medieval manuscript leaves sold on eBay from books broken up on purpose to make money from the sales of leaves as commodities for "collectors" rather than as part of the book, itself. Most leaves are from horae but some come from breviaries.
Medieval music in MSS: Again, not exactly an "archive," but a work-in-progress I have been developing based on some manuscript leaves which contain musical notation. Musical notation and text punctuation have common origins in the earliest manuscripts which record texts intended as performance prompts for reading/singing aloud. Special purpose musical manuscripts serve important functions in the Medieval Christian church, especially the "antiphonaries," huge paired manuscripts meant to be read at a distance by dual antiphonal choirs who sang the original "stereo" music performances during church services. Smaller MS music notations also are found in prayer books like the horae (books of hours) and breviaries.