I just experienced this problem after applying the latest patches to Office 2003. I opened a template I use often, and my signature had been inserted at the top of the message.
I tried using a different template, and on that one my signature was inserted at the bottom of the message. This seemed more logical, although since my template already included the signature, it was now there twice.
After some testing, I discovered that if the template is in Rich Text format, the signature gets inserted properly at the end. But if the format is Plain Text or HTML, it's inserted at the top of the message.
Apparently this is a new behavior of Office, and it would be useful if it worked properly. I have many templates that I use, and it was always a pain when my signature changed, since I'd have to update each template individually. I've sent a message to Microsoft support regarding this, and am awaiting a reply.