My brother and I would like to store our backup files on each other's
home computers.  Ideally we'd use FTP (or something more secure) to
copy the files after the backup job completes.

It seems like an elegant way to get our backups "offsite" given that
we will probably always have spare hard drive space on our machines,
however it appears to be a difficult thing to do given that we get
dynamic IPs from out ISP.

We are both running XP home and are on the same (cable) ISP.  We both
also have firewalls: mine a Dlink router and his a software firewall.

Also, if it helps, we own a couple of domain names and have control
over the DNS for the domains and subdomains.  If it were not for the
size of the backup files compared to the capacity of our web server
we'd just use the web server as a relay for the files.

Have you heard of Gnutella? It is commonly used to download music
illegally, but it is supposed to be used for the purpose you
described.

the software system teleback will help you with that 


http://www.hallogram.com/teleback/

TeleBack is a complete software system that will allow you to provide
automated Remote Backups as an additional service to your existing
clients or other businesses in your area. You can relieve your clients
from the mundane task of having to do their own backups by allowing
TeleBack to do it for them after business hours automatically.

graft-ga,
thank you for your suggestion.  i'm hesitant to use these types of
tools due to security concerns.  maybe i don't know enough about them
but i'm under the impression that these tools create massive security
vulnerabilities for the host.

kevinusa19,
thank you too for your suggestion.  from what i could ascertain from
the url you gave, this tool uses modems and phone lines to transfer
the data.  this would be prohibitively slow for my purposes.  it also
seems a bit expensive given that i can buy a 30GB usb hard drive (yes,
i'd have to take offsite myself) for less money than this tool. 
thanks again though.

Here is a suggestion. Run FTP daemons both of your machines and make
sure you use secureftp as the client.

Server:

http://support.jgaa.com/index.php?cmd=DownloadVersion&ID=1

Client:

http://security.sdsc.edu/software/secureftp/

You may have to open port 21 (default ftp port) in your firewall. I
would suggest to change the default port to 2121.


Also if you are behind a router (netgear and you get ip such as
192.168.x.x then you may have to open port forwarding as well.


Hope this helps