I am to reinstall an old Windows XP installation. Before I format the drive, I have to backup some data (~200GB) like .doc files, pdfs, photos to an external hard drive. My concern is that this installation might be infected. My presumption, or rather fear, is that if it is infected, the infection might live on in the backups. What would be the best way to backup these files so as to minimize chances of carrying over an infection?
A first point is that the files shall be copied under some protection. When you boot up an infected system, malware and virus present on the system may be activated, and then try to propagate, for instance into other files on an external hard drive.
Infected files are said such because of their ability to "infect" computers which look at them. Precisely, a virus in a file fools a computer which "opens" the file into executing its nefarious code. This fooling uses vulnerabilities in the software used to interpret the file contents. Unfortunately, running weak software can be quite automatic: for instance, if you use a Windows system to have a look at some files in a directory, then the file explorer will show miniature versions of pictures. This means that there is a part in the file explorer application which automatically reads and interprets the picture file contents. Any vulnerability in that interpreting code will allow a virus to propagate, even if you, as a human user, do not actively open any of the files.
Ideally, you would like to first copy the files from a completely distinct operating system, e.g. Linux (under the assumption that a Windows virus won't harm Linux, and vice versa). You could boot from a CD or USB stick a Linux system (e.g. Ubuntu's desktop edition install CD is also a usable OS which can work off the CD without installation). Alternatively, open up the Windows machine, extract the hard disk, put it in a USB hard drive enclosure, and plug it into a Linux machine.
Then, the files ought to be scanned for known viruses. There is never any guarantee that all infections will be detected by any antivirus, but they can still help. In particular, if you keep the old Windows XP out of any network contact, or (even better) simply shut down for a fortnight, then any virus on it will be necessarily at least two weeks old, giving more chance for antivirus to have caught up with it and to successfully detect it.
If you are still wary of virus, you may apply some transcoding on files. For instance, a JPEG picture can be converted to PNG, then back to JPEG. Even if the original file includes some sort of virus, the conversion from JPEG to PNG will remove it, if the converter application is not itself vulnerable (i.e., do that from the Linux system with which you copied and scanned the files). Transcoding can incur some information loss; Word files would be problematic.