The MIT Libraries have many scripts from a range of playwrights. Unfortunately, there is no good way to pull up an exhaustive list of what we have online, but there are several ways you might locate some of what we have.
If you have a particular script or author in mind, you can do either a title or author search in Barton, our online catalog:
The New Books Display (1st floor, Hayden Library) and Browsery (2nd floor, Hayden Library) contain all of the most recent play scripts in our collection, and are easy to browse (although note that both collections contain lots of new books in all fields--plays are interspersed among them). Check the PR call number range for British and the PS call number range for American playwrights. Almost everything else will be in the basement of Hayden, but isn't easily browsed (although because of their size, scripts usually stand out if you're looking).
MIT's WorldCat now allows you to borrow directly from other area libraries in the Boston Library Consortium (BLC) - just click on the "request" button next to the box that lists the BLC libraries that have the script you want: