Simple question. I have TurboTax software for several years on my computer. Is there any need to keep this older software?

Just in case you want to amend a year or see your actual entries.  Be sure you have saved the pdf files for each year before you uninstall.

Make sure you have saved both the .tax and .pdf files for each year.  Your tax files end in .tax or .tax2017, .tax2018 or .tax2019 etc.  They should be in your Documents in a Turbo Tax folder.  You should also have the pdf files of each year.  Or search your computer for all files ending in .tax.  Also if you haven't done it,  I would open each year in the program and save it as a PDF file, go to File-Save to PDF so you don't need the program installed to view or print your return in the future like to get a mortgage or loan, etc.