Suppose I have a lot of data I want to backup at pc A and pc B (and C and D...). 
All are connected over a network to pc Z.
How can I backup the data with Z, but not as a full copy of A+B+C but
only as parity information made by combining A,B,C, essentially doing
something similar to what a raid(4?) does, but with multiple PCs over
a network, and not in realtime.

The advantages would be that Z would not need as much space as A,B,
and C combined, but only as much as the largest of them.
with reed-solomon-like parity data (http://parchive.sourceforge.net),
the storage usage and redundancy could further be improved.

I realize that this would be less secure than a regular backup, and
not recomended as the only solution for critical data.


I don't need the real-time aspect of a real raid, the backup process
could be run every couple fo hours, or whenever large changes on
several systems make a new parity set necessary.

pc Z could run windows or linux with custom modifications, but A,B and
C should preferably just need windows fileshares and not require any
custom software (such as a Network Block Device driver)

Which software or set of tools could accomplish this?

There is an open source software package that does something similar to this.

It is called BackupPC (http://backuppc.sf.net).

It will back up a PC's file, and create a "pool" of common files. Any
file with a matching hash or checksum, will be considered identical,
and if the file is already archived on the backup machine, a link is
placed.

This alleviates the need to have an individual copy of "ls" for each
machine you are backing up.

I use BackupPC and love. Even has a web based admin for reviewing
backed up files and restoring the files over the network.

Hope that helps.

that is very interesting, thanks

However it is not exactly what I was looking for, because this method
only works for identical files, which would be mostly system data. I
the end I was hoping for something that can reduce storage capacity
for user data too, by not saving all the data but only parity
information.

nevertheless, this seems usefull. and it does not require client side
changes. will check it out.