The University of Nebraska-Lincoln Libraries have numerous books on board games including:
Board and Table Games from Many Civilizations
New York: Oxford University Press, 1969
Love GV 1312.B42
A History of Board-Games Other Than Chess
New York: Oxford University Press, 1952
Love GV 1312.M8
The Oxford History of Board Games
New York: Oxford University Press, 1999
You can find books on particular games by looking them up directly in the library catalog.
For example, a subject search for "Chess" turns up numerous books about chess and related subjects.
Books, theses, and dissertations available in libraries around the world are listed in the WorldCat database. Books listed in WorldCat which are not available in the University of Nebraska-Lincoln Libraries can be easily requested through Interlibrary loan. A "Request via ILL..." link is available in the detailed citations for each entry.
Searching article indexes like JSTOR and Academic Search Complete will yield many articles on board games or on particular games. Articles in JSTOR are available in full text. Some articles in Academic Search Complete are available in full text. You order articles listed in Academic Search Complete which are not available in full text easily by using the "WebBridge" link and then clicking on the "Interlibrary Loan Request" option. Interlibrary Loan is fast and free to N-Card holders.
Board Game Geek is a large wiki devoted to the board game genera. The wiki is very thorough, containing many articles.