Go to S & P Indices
Click on Indices by Asset Class to browse indices.
For example click on U.S. under Equity.

Once you've selected the index you want (ex- S&P 500) click on the grey tab Constituents to see a list. You can also export the list to excel.
 

Use Bloomberg, available in the Margolis Market Information Lab (MIL) at the Business Instructional Facility (BIF).

• Type ADD and press GO for Historical Index Additions and Deletions

To inquire further please contact: bis@library.illinois.edu

For archival research: one can also look at the print source: Security Price Index Record (call number -- Main Library Stacks Q332.6 St24t2).
It contains the S&P 500 companies and the years they appear in the Index.