These databases are openly available online.
Art Song Central: A searchable/browsable archive of free, printable, public domain art songs. Includes key, range, IPA transcriptions for every German, French, Italian and Latin song in the index.
Choral Public Domain Library: Not just choral music. Contributor-generated (wiki) PDFs, midi files and more. "You can use CPDL to find scores, texts, translations, and information about composers."
CosandScores: Public domain works collected and digitized by pianist Walter Cosand.
Digital Music Collection, Sibley Music Library: The Sibley Music Library at the Eastman School of Music (University of Rochester) has an extensive digital score collection with stable URLs which may be printed and downloaded. They also have a link by which you may request the digitization of a public domain score in Sibley's collection.
The Henselt Library at European-American University: Public domain scores of rare nineteenth-century piano music: PDFs of over 2,000 rare scores of nineteenth-century piano music, many of which are not generally available elsewhere. The Henselt Library consists of public domain scores that are mostly for piano 2 hands, with a small number of concerto scores and reductions.
International Music Score Library Project (IMSLP): The goal is to create "...a virtual library containing all public domain music scores, as well as scores from composers (living or otherwise) who are willing to share their music with the world without charge." Contains not only full scores, chamber music parts and scores and vocal scores, but also now includes orchestral parts. More being added daily. Includes the Werner Icking Music Archive contents.
Internet Archive: Contains a surprising number of scores, particularly piano/vocal scores of operettas.
The Lester S. Levy Collection of Sheet Music: A treasure trove of popular American sheet music. "The collection spans the years 1780 to 1980, but its strength is its thorough documentation of nineteenth-century America through popular music."
Music Library Scores Collection: Made available by the University of Michigan Libraries. Comprised of over 1100 scores held in Music Library's general and special collections. Understandably Michigan-centric.
Online Resources for Music Scholars: Digital Scores: An insanely complete clearing house for digital LEGAL scores. Includes 78 (yes, 78) sites providing access to public domain scores, manuscripts, facsimiles, you name it. Some sites also include other documents and audio files. Contains many of the sites listed below.
The Open Hymnal: "This hymnal is a part of the Open Hymnal Project to create a freely distributable, downloadable database of Christian hymns, spiritual songs, and prelude/postlude music." Updated June, 2014. A wealth of information about public domain hymns plus PDFs of the hymns. (Link directly to the PDF.)
VARIATIONS Prototype: Online Musical Scores: From Indiana University. Viewable public domain scores with stable URLs. Easy navigation of the scores, but not set up for printing.