Is there software (hopefully freeware) that counts how many characters
I type per day at work. Detects what words I use the most, and the
program runs as  background process.

Being a Microsoft Word geek, I'd say that it'd be pretty
memory-hogging to track everything you type. We'd have to get all the
words you type into a database as you add them. Now, if you wanted to
count, for instance, the number of times you used "Smithsonian
Institute", we could do that. If you had a list of Words somewhere, we
could get you a count of how many times you used them. This would be
fairly simple with a Word macro.

You can count how many characters you typed in a Word document and, on
save, we could catch that number into a file that you could review
daily.

To summarize:

I doubt you'll find software that'll do it simply because it would hog
so much of your resources to count all the words so it can show you
which ones you use most. And I doubt you'll find anything that counts
characters because all the Word Processors pretty much have that built
in.

BUT, you should let us know what you're typing in, if specific
programs, so we could at least help you have a look around.

I am a software developer, and understand the consequence of such
program. I also know that it is possible. I have used software that
tracks people's usage of computer on the background.  The program kept
information about time and words typed during the day for employee
management purpose. It even kept screenshots of the person's activity.
 I do not need such robust program to monitor, but looking for a
program that can count how many words I type per day so I can monitor
people by couning and keeping statistic of "words typed per day"  Is
there such program out there that I can use?

http://pulse.whatnet.org/ is a website with software that tracks it.
many people on forums use the software and have their statistics
displayed in their signature.  that software is located at:

Thank you for the link.  I have tried it, but was wondering how secure
the program is.  This program is not open source, and I had to sign up
for an account providing my email address.  For the case of handling
sensitive data, I am not sure if I can really trust this software; do
you?