Internet-based answering machine that can intercept your incoming phone calls and take messages while you're using your internet connection. You can screen the call to voicemail, or pick it up. Free 30-day trial.
eFax gives you a private local or toll-free fax number in over 35 countries. You can send faxes via email, and incoming faxes are also sent to you by email so you never need a fax machine. You can try the service free for 30 days (send up to 30 fax pages and receive up to 130 pages).
Skype lets you make totally free phone calls over the Internet. You can also chat and send files to other users. For a small fee, you can add voicemail, call from your Skype client to normal phones at dirt-cheap rates, or even get a dedicated phone number which automatically forwards calls to Skype.
This email to fax gateway lets you send free ASCII text faxes via email to many countries around the world. The interface is quite complicated, but it's free so it's hard to complain...