If you need a copy of a play, the fastest way to find it is to do a Title search on SAGE, the library catalog. If you want to see all of the materials the library owns by Shakespeare (we have many different editions, printed by various publishers, with different editors, criticisms, introductions, forewords, prefaces, afterwords, etc.), do an Author search for Shakespeare, William. The library has over 1250 individual titles "by" him. Or, go to the lower level (basement) of Morgan Library and browse between PR 2750 and PR 2839. There are twelve bookcases' worth of books--criticisms, commentaries, etc. (There are two shelves on Hamlet alone.)
A very useful multi-volume reference book is the:
Shakespearean Criticism: Criticism of William Shakespeare's Plays and Poetry from the First Published Appraisals to Current Evaluations. 110+ vols. PR 2965 .S43 Reference
At the back of each volume (use the most recent one), there are three indexes: a cumulative character index, a cumulative topic index, and a cumulative topic index by play. Multiple viewpoints from scholars and commentators. Vols. 1-10 give historical overviews; 11-26 performance history of plays on stage and screen with eyewitness reviews; 27-56 have criticism published after 1960, with each volume having a theme such as politics or religion. Vols. 57- are works-based, a play or poem, with some topics intermixed, such as madness or war. (Again, use the cumulative indexes.)
World Shakespeare Bibliography Online. CSU affiliates only.
This database "provides annotated entries for all important books, articles, book reviews, dissertations, theatrical productions, reviews of productions, audiovisual materials, electronic media, and other scholarly and popular materials related to Shakespeare and published or produced between 1962 and 2008." There are currently "more than 114,231 records in this version." Use advanced search to look for words in title, etc.
Criticism of individual plays can be found by doing a LC Subject search for:
Or, do a LC Subject search for the title of the play:

Note: By definition, individual plays are a subset of Shakespeare's works. So be sure not to overlook possibilities under "Criticism and Interpretation" (below).
Criticism of Shakespeare overall can be found by doing a LC Subject search for: