I am looking for a secure FTP program.  If I purchased this Cute FTP
http://www.cuteftp.com/cuteftp/ would it still be secure if my server
does not have SSL technology?  Is there another program is that is
SIMPLE and SECURE that would work?

There is a secure file transfer protocol called SFTP that runs over
SSH (not SSL). It is a client-server based system, so you need both
client and server software for your respective PCs. Both clients and
servers come with most Linux systems and probably other UNIX-like
systems.

Freeware clients are available for Windows platforms:
Putty http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html
WinSCP http://winscp.net/eng/index.php

Free servers for Windows don't seem to be common; here is a link to a
document that explains how to run a UNIX version on Windows:
http://pigtail.net/LRP/printsrv/cygwin-sshd.html
The sponsored links I'm seeing right now suggest there are several
native versions but not free.

Actually there is ftp over ssl as well, it's commonly refered to as
ftps.  However, SFTP which is ftp over ssh is far more common.

As the other commenter noted, whether it's sftp or ftps in order to
benefit from the advanced security both the client and the server have
to support it.

CuteFTP is pretty simple, but you'll need to get the pro version if
you want the option of having sftp available in addition to ftps.  You
could also try filezilla, which is a freeware graphical ftp/sftp
program:

http://sourceforge.net/projects/filezilla/  

However, there is no solution that will be secure without also having
server support.  After all, how would that work?