The major company I work for has had a long standing goal of becoming as completely paperless as possible. I won't disagree with the comment in the previous reply about saving your original data, as I am not in that specialty area.
That said, if you take data electronically, you could also save electronically.
The catch with saving everything electronically (which I support), is that you need to have adequate measures to assure you don't lose data. We have a very extensive system of backups to a level where it sometimes gets pretty annoying.
Our document control is set up where the electronic copy of a spec, held in the electronic repository is the official copy, and paper copies are considered "Uncontrolled" (unless you make allowances in individual cases).
Our official reporting is web-based, and the servers used to hold all the web-based information are in a well operated back-up system.
I would even contend that hand written paper copies could be scanned, put into PDF (or TIF, JPG, GIF, or what ever works best), then electronically archived.
With the right operational safeguards (i.e.: data security, good backups, etc..) that a paperless system is easier to deal with. You could be in an office in China, an auditor wants to see original data taken in a lab in New York two years ago (assuming your record retention policy requires that data to be retained). In an electronic data retention system, you could easily pull up the original handwritten document in electronic format for the auditor.
I'll stop short of saying that you could dispose of the original piece of paper (based on the previous reply). I wonder whether in such a comprehensive documentation system whether even in his circumstances you could legitimately discard the piece of paper and archive the electronic facsimile of it? I'm not sure on that one.
My company, by the way, is QS9000 (soon TS16949).