French National Library in Paris have put up a part of their manuscript collection online here. Some of their Hebrew manuscripts are online as well here. Just search for “hébreu” and they will pop up.
HebrewBooks.org just announced that they opened up a new website dedicated to Hebrew manuscripts called HebrewManuscripts.org. So far they have 1000 manuscripts from the JTS library. Each manuscript can be downloaded in a convenient PDF. Unfortunately the manuscripts are scanned in 2 color, like books, and are not high resolution so some of them are either very hard or impossible to read. Hopefully they will improve the site with time and will put up color, high resolution scans. It’s a great start.
Munich Library Hebrew Manuscripts are available for free download from their website here including the famous complete Talmud Bavli Manuscript – Munich Cod. Hebr. 95. When you click on each manuscript in the right upper corner there will be a link PDF-Download. Click on it and it will make you a single PDF file with the whole manuscript with high resolution images.
You can also browse or search their manuscripts database here and download what ever you can find. Keep in mind that all manuscripts are cataloged in German so the spelling of many titles or descriptions is not the same as it is in English.
The complete list (in German) of all Hebrew manuscripts collected by the Munich library until 1895 can be viewed here.
Not all of them have been digitized yet, but if you check back on their website they will probably start showing up soon.