My vote goes for having an APPROVED BY table in a document. Just collect approvals by email and modify the document yourself. That way you don't have to organize a chain of emails to pass a document around. If your document repository allows, approvers could modify the document themselves, or a link to the related email is a good idea. If not, at least keep the emails in an archive for audit purposes.
A lot of the time the actual approvals are not as important of the audit trail of related emails. That archive of threads would be a distraction from the document's content. Although I hate it, I've frequently seen required approvers just too busy to formally deal with the process. In those cases you have to make sure you have a record of "please reply with your approval" requests that to explain that empty row in the APPROVED BY table.
