Oh gods yes!
Anything signed is kept.
The Terry Pratchetts I'm finding really hard to let go of because they took me so long to get (and I now have all of them digitally).
There are a handful of books which have a huge emotional resonance (like my Charlie and the Chocolate Factory which is the first book I remember reading).
However, the vast majority are kept because there is currently no electronic edition (legitimate or otherwise). I think publishers are missing out by not speeding up the digital publication of their back-catalogue.
T