I keep forgetting my passwords & telephone numbers, and loosing the
paper records where I write them down. So I decided to keep them in a
text file. I have Norton Internet Security. Can spyware or other
malware extract information from a text file? If yes are they safer on
a floppy? Can malware plant files which will extract copies from a
floppy while not connected to the internet?

yes a spywere can read your text file
one way is save them in the secure Database and set a password for it
next way is : comperessing the text file in Winrar program and set a
password for the rar file and keep it in the floppy or CD
in two way you have to secure your PC for this use Norton Anti Virus
and Norton Firewall and install the lasted servis path and Hotfix and
you have to fix bugs in your PC for scanning your pc for security bug
you can use the Nessus Windows version(Tenable NeWT)
you can Download it from http://www.nessus.org/download/

Password Safe is a free program that stores passwords in an encrypted
file, which you access with a single password (but don't forget that
one!). It is available from http://passwordsafe.sourceforge.net/

It isn't designed to save phone numbers but you could either enter
them as passwords or enter them in the associated note area.