If you have a citation for the United States Reports (usually abbreviated to US), the full text of the bound volumes can be found from volume 502 (1991) onwards at:
Supreme Court judgments can also be found in the Lexis Library with added page numbers for the US Reports. Coverage is from 1790 onwards.
From the Lexis Library home page use the 'Find a Source' box to search for 'Federal Court Cases, Combined'. Then select the source and OK to go to a judgment search page.
Findlaw page at http://caselaw.findlaw.com/court/us-supreme-court also provides access to Supreme Court judgments. Docket numbers are included, but without citation details and page numbers for the US Reports.