The National Centers for Environmental Information (formerly the National Climatic Data Center) stores recorded weather radar data, and the archives are free to access.
See also this website for weather animations:
A problem: The data files are compressed in a format native to Linux (including Apple). Windows does not recognise the zipped files. If you can unzip downloaded files, then the following BB4W program will display the contents, as an image.
Not so much of a problem: In order to access the data via a user-friendly format, the standard process was to use a combination of tools to convert the archived files to 'NetCDF' and then into multiple, plain ASCII tables. The program below reads the original archive format, without the need for additional tools or conversions.
Limitations: Okay, so we can skip the usual conversion process, but this simple program is limited to displaying Hi-resolution images created from type 31 messages (Level II reflectivity only), which are not found in legacy data files from 2008 or earlier.
While useful specifications are to be found on the NCDC site, some analysis was required to interpret the archive format.
This link downloads a zipped folder containing one (pre-unzipped!) data file for Hurricane Arthur, a compiled version of ArchivePlot and a text file containing the source code.
Notes: Place the ArchivePlot program in a folder containing unzipped NCEI archive files. The program automatically locates any files without an extension and reads them, one by one, creating bitmap images of the same name.