I am looking for sites that offer free non-animated gifs and some free
gif creation utilities. I am only interested in non-animated gifs.

Most applications designed to work with pictures have the ability to
save files, or export them, as gif's.  Even Microsoft's Paint program
can do that. If you are needing to convert a file to a gif from
another format then here is a great, free utility that can open most
kinds of image files and save them as a gif.  It also has basic
editing tools.  Install and download it along with the plugin, which
gives you more file type options.

http://www.irfanview.com/

This software is for creating and modifying gif's.  You should be able
to take an animated gif and make a non-animated gif out of it.

http://www.gif-animator.com/?ga-ggl&gclid=CKiH_97l7oUCFUX0JAodlUdMvQ

There are lots of sites with animated gif's that you could then modify
to a non-animated file.

http://www.gifworks.com/

http://gifs.net

I am a little confused as to why you want to find non-animated gif's. 
If you are after a still picture a jpeg will be a smaller file for the
same quality and size picture.  That is why you will have a hard time
finding "non-animated" gif's out there.  A non-animated gif is really
just a single frame animated file.  Since it has only one frame it
doesn't move and appears "non-animated".

That being said, you can make any image into a single frame gif file
with the utilities listed above.

If this answer does not fully satisfy you please post a request for
clarification with more specifics and I will answer it promptly.

Thanks!