We've been lending board games for one-week checkout at my library for about a year. I know of a handful of others that do this or are in the process of beginning this service. If your library (or one that you know of) circulates board games, let me know. I am compiling a list that I'll be updating on Tumblr. When trying something like this that seems to have some risk built into it (i.e., "Won't people lose all the pieces?"), I've found that it's helpful to know that there are others who have done it and that I can reach out to them with questions.
You can respond here on the forum, contact me via Twitter (@pjbntly), or email me at pjbentley@gmail.com.
Thanks!