We normally do not, unless a project calls for it. I can count on one hand how many times a project has called for a suffix in the seven years I've been indexing. In those projects, they had a field for the suffix.
If you have John Smith, then have John Smith, Jr., you will only index the first John Smith because the second John Smith is a duplicate (even with the suffix) of the first John Smith.
Only when there's a specific field to index for a suffix, but we never put suffixes in the names fields.
Thank you so very much, Barbara. I tried looking everywhere for an answer. I could not find anything about it in the General Indexing Instructions. I appreciate your help.