I thought it would be nice to list and discuss some digital resources that are freely available. Every one of these has been useful to me.
1) Google Books.
Definitely the king of free digital resources. It keeps getting better, not only becoming more comprehensive, but better features are constantly being added. Unfortunately it is a great big jumble, requiring one to become adept at searching. Still, I imagine they'll devise solutions for this. In the meantime, to use it properly it's important to master search.; titles, authors, dates, key words, with a variety of spellings, etc.
2. Hathi Trust.
Google has an interesting system. In partnering with great libraries around the world, Google ''pays'' those libraries in the following manner: in exchange for opening up their priceless collections for digital scanning, with Google owning a digital copy of each work, Google gives each library a digital copy which they own (I think). Basically what's in it for the libraries is that Google is scanning their collections for them at virtually no cost to them. I'm not sure what process Google goes through to clear each book for adding to their database, but very often you can come across a book on Google with all the data indicating where and when it was scanned. For example, it might say that the book is from Harvard's library and it was scanned on May 3, 2009. But the book is not online yet. Presumably each book has to be legally cleared and/ or there is a backlog. But I've come across many books like that. A couple of years ago I noticed that only one university library -- Michigan University -- seemed interested in making their books which Google scanned available on their own servers, integrating them with their catalog.
Enter the Hathi Trust. Hathi's formation was not motivated by the use I've found for it (which I'll spell out) but to address a simple, fundamental question: who says that Google Books will be there forever, or will always be free? In fact, Microsoft had a digital project (books.live.com) which it abruptly killed once it realized it could never compete with Google Books. Overnight thousands of freely available books scanned by Microsoft disappeared. So the Hathi Trust aims to be an alternate repository of books scanned by Google. Libraries need only sign up and add their collections. Only a small number of libraries have joined, but more join constantly. Early on Michigan U joined. Columbia University recently signed up. So what I've found is that sometimes books which were scanned months ago but not yet on Google are on the Hathi Trust. In one case, I was able to download an important book which wasn't available on Google for over a year. Incidentally, the Hathi Trust is especially good for users outside the United States who face additional restrictions on Google Books, in many cases they are not even aware that the version they use, whether in Europe or Israel, is skeletal. So after checking Google, check the Hathi Trust.
Archive.org is similar to Hathi in that it also includes many books digitized by Google (in case Google disappears or goes rogue, you betcha) but includes much, much more. Some smaller libraries that aren't likely to be approached by Google have modest digitization efforts of their own, and share them on archive.org. Other large libraries simply don't want to deal with Google, yet want their digital offerings available. There are thousands of Yiddish books via the National Yiddish Book Center; many of these works are as orphaned as they come, but as they were printed after 1923 they will never be available in their entirety on Google. In terms of free resources, I would place this behind Google (Hathi is more the place to go once you've ascertained that a book was scanned by Google in a library which participates in Hathi, yet isn't on Google; this would apply to Michigan U, but not Harvard).
6) Hebrew Books.
In a class of its own. I hardly know where to begin, but anyone who is interested in seforim ve-sofrim knows what I mean.
7) Seforim Online.
Back when HebrewBooks.org was "only" a repository of seforim printed in America, with some miscellaneous RCA handbooks and the like, Seforim Online was a modest in size, rich in content, archive of rare and interesting seforim, from Menasseh of Ilya to Christian David Ginsburg. Although it is not what it was since so many other resources have sprouted and supplanted it, occasionally it comes back to life, e.g., not long ago scans of some valuable Hebrew Bible codices appeared on the site, which are unavailable elsewhere.
8) Compact Memory
Compactmemory.de is an amazing archive of German Jewish publications encompassing approximately the years 1800 to 1940. It isn't comprehensive, and as more time goes on many of its offerings are on Google as well, but there are treasures on Compact Memory. Many a footnote has sent me there.
The JNUL has an excellent, selective digital archive. They're constantly adding things, and the scans are of very high quality. Great for first and early editions, and their basis -- the JNUL library itself -- is a deep well which promises great offerings for years to come. Unfortunately their files are not available in pdf, which is a little annoying, but you can download entire books as djvu files for viewing on your own computer. In addition, there are archives of six important early Hebrew newspapers, and a nice collection of Ketubot and manuscripts. For this purpose (Hebrew and Jewish newspapers) see also the Historical Jewish Press site from Tel Aviv University.
10) Judaica Sammlung Frankfurt.
This web site contains hundreds, if not thousands, of European books of Jewish interest, primarily German, but many are in English, French, Italian and Hebrew. When Google and the others fail, Judaica Frankfurt doesn't let down.
The Bibliothèque nationale de France's digital collection contains many rare books and periodicals.
12) Bavarian State Library.
This is where the digital Munich Talmud is; but it also contains excellent scans of rare Judaica and Hebraica.
13) Gottinger Digitalisierungzentrum.
14) Universidad de Sevilla.
15) Internet Library of Early Journals.
16) Making of America pt I and II.
These are university libraries with digital collections. It's not like I visit them daily, but these and others are reminders that if you're looking for something online, you must never assume it's unavailable. You simply must dig deeper. In my recent post on early printed images of the shekel I used Google Books, the JNUL and Seville University; it's not like I have Arius Montanus' Antiquitatum Judaicarum Libri IX (Leyden, 1593) sitting on my book shelf; but it's also not on Google Books. Remember, these are only the tip of the iceberg. Dozens and maybe even hundreds of universities have digital projects. Also, these resources are unique to my interests. There are countless free digital collections containing much material of interest to you.
16) Simonsen Collection at the Denmark Royal Library.
17) The Braginsky Collection.
Both of these are one of a kind, since they include unpublished manuscripts of great worth and interest.
Edit: I think it's a good idea to add resources as I find them.
18) The Leiden Manuscript of the Jerusalem Talmud.
19) The University of Haifa Library has a modest digitzation project which is just getting underway. with some interesting titles.
20) Various zeitschriften.
Also, many periodicals are available. Just because it seems obscure, doesn't mean it's not worth googling and checking past the first and second pages. I've discovered that much is available if you know what to look for and you actually look.
Finally, network. You never know who has what, who has personally scanned something, or received something from the author or publisher directly. If you develop or join a group of like-minded individuals whom you can ask "Have you got this?" your chances of acquiring what you're looking for goes up. You will likely find that people are happy to share what they have.
Remember, all these are perfectly free and don't require any subscriptions. There are certainly hundreds of thousands of free books and periodicals in these resources. In a matter of hours you can probably find 100 books of great personal interest, you only need to look. Subscription resources will be for another post.