Diane253:
Has anyone looked at this as using the modem for a fax machine? I would like a Fax machine that saves the fax to a memory device so as to retrieve the information later by a PC so you can print only if wanted to do so. I get too many junk faxes which is just a waste of paper.
Good idea and easily doable using such shield because it will use voice/fax modem chip , So far 30696 views and counting but noone brought this idea to life 
It can also be used as
1-Cold Caller Blocker
2-Telephone recording with Caller ID
3-Fax receiving/saving (as you suggested)
4-Answering machine
5-Interactive voice response system
6-Home automation over landline
7-Foundation for Arduino based PABX
8-DATA Communication
9-Auto dialer (Connected over blutooth to smart phone's phone directory)
10- GSM to Landline gateway
11- Smart Telephone set
12- Call forwarding