Dan
Spaces should be OK from version 10 on-wards.
In most cases the tool will throw an appropriate error or warning, for example, a field name in a fGDB that has a space will cause the following to be thrown;
The field name that you intended to add to your feature class or table is invalid and has been modified accordingly. Using invalid characters within a field name, such as spaces, are a common cause of this error.
If you come across any please contact Esri Support.
Thanks
Steve