Experts and BHG readers answer.
Are there any sweet gum trees that don't produce those spiny seed balls?
American sweet gum (Liquidambar styraciflua) has male and female flowers on the same tree, so every tree can set fruit. There are a few cultivars that make a claim of bearing "few fruit," but they aren't common. You may have to search for them. Cherokee and columnar 'Shadow' are hardy to Zone 5. 'Rotundiloba' is hardy to Zone 6.