This depends primarily on the size of your genealogy file. A smaller file, less than 2500 individuals, requires...
Windows 98 or better
32MB memory or more
130Mhz or better Pentium II
It's possible that smaller files will also work on machines with less memory (say 16MB), but we haven't tested that.
If you encounter environments where you don't think GenSmarts on a particular machine is usable, let us know - email@example.com
For information about non-Windows versions, see the post in the FAQ on that topic.