The SPSS people have spent at least 30 years developing their software, so don't expect to find anything free that's close.
But if you have specific kinds of statistics in mind, there are lots of choices. Many have been developed by academics who put the packages together with grant money. That often means that they are not allowed to sell it commercially. And, yes, there are some open source alternatives.
Use this site as a starting point...
http://freestatistics.altervista.org/en/stat.php
However, I can't emphasize enough that whether you acquire free or commercial software, the user needs some solid statistical training.