More and more journals require researchers to share the data that supports the tables and figures in an article, even if you don't have a grant that requires public access to the data. There have also been cases of journal retractions for lack of supporting data more than 10 years after publication.
Even if you deposit your data (see box below), it is a good idea to keep your article pdf, doc*, and data together in a folder.
The Readme file should have all the background information about the data so anyone who looks at the data can figure out how you analyzed it to get your results (more in Organizing and Documenting Your Data). This is part of the Rigor and Reproducibility policy the NIH is promoting.
*Keep the final peer-reviewed manuscript in case you need to deposit it for public access, not all publishers remember to deposit articles, even if you have indicated you are grant funded (see Compliance Research Guide for more).