I am using Fedora 14 right now and find some software in the fc14 repository is a little old.
I need some software in my machine to be updated, say, to the Fedora 19 version.
Without upgrading the system, what is the best practice to do so?
You have to update your system, or you may run into kernel incompatibilities. Seriously consider upgrading. If Fedora updates too much for your needs, consider using CentOS or Scientific Linux. Fedora 19 is in Raw Hide status at the moment. The current stable release is Fedora 18