The Art of Computer Programming, Vol 3, "Sorting and Searching", by Donald Knuth, 1973. My copies of the other volumes of the book are more recent (the 1990's). I bought Vol. 3 second hand, I believe.
Otherwise, K&R's The C Programming Language, but the only second edition (1988).
Comment on Re: The oldest computer book still on my shelves (or on my digital media) is ...