I want to backup my files in Ubuntu 12.04 to an external drive in a way that they are accessible from my wife's computer which is not Ubuntu, it's Windows. How do I do that? I don't want any compression or encryption, just the files in their trees in a way that is readable when the external drive is connected to a Windows-based machine.
To save files for importing to a Windows OS the easiest would be to just format the external drive with FAT32 or NTFS and copy your files there. By this all files and their trees will be accessible from any Windows computer.
However with this method you will loose all Ubuntu file permissions. It is therefore not advisable to copy these files back to Ubuntu, it is more a one-way solution for sharing files from Ubuntu but not from Windowsb back to Ubuntu.
In case you need to keep your file permissions you will have to format your external drive with e.g. ext4, and install software on the Windows computer to read an Ubuntu file system:
The issue you have here is the filesystem you need to choose. The systems where the different OS's are default happy with are not compatible, but there are ways around this.
The easiest is to format the disk in FAT32. This is a bit old, and you will have trouble with big files. There is a quite low upper-file-size limit of 4 Gb. So if you have DVD's, blu-ray or the like, you might get in trouble.
You can also use the windows-filesystem (NTFS) for linux. There used to be some trouble, but there is support for it now-adays. Choose this if you can't use FAT32
I would advice against choosing one of the 'default' systems from linux (EXT3, ReiserFS, etc) as their support in windows is limited to non-existend. WIth the above 2 options your wife will not have any problem reading the disk.