You could add it to the form's clean() method:
class ThingForm(forms.ModelForm):
    def clean(self, *args, **kwargs):
        cleaned_data = super(ThingForm, self).clean()
        owner = cleaned_data.get("owner")
        other_things_count = Things.objects.filter(owner=owner).count()
        if other_things_count >= 20:
            raise forms.ValidationError("Too many things!")
        return cleaned_data
Alternatively you could overwrite the models save() method, or you could create a signal that is fired on pre_save, but neither of these will allow you tie validation messages to the form, so I think the clean() method above is best. 
EDIT If you want to exclude editing, you can check to see if the ModelForm has an instance, i.e. an existing object
other_things_count = Things.objects.filter(owner=owner).exclude(pk=self.instance.pk).count()