Click Rankings and select a specific year, includes 1996-Present.
For free access to past lists from 1930-2016, see here.
Alternatively, you can request physical or digitized copies of past lists through Western Libraries.
Nexis Uni: You can produce a list of Fortune 500 companies. Using the Menu drop-down at the top of the page, choose Company Dossier. Then select Create a Company List. Use the Top companies drop-down to select Fortune 500 or 1000 only. Add other criteria as needed and search.