Effects of Upgrading OpenSSL library?

we are having a Redhat linux server network proxy server [Apache http] with openssl version standing on

[jae@myserver~]$ openssl version
OpenSSL 0.9.8e-fips-rhel5 01 Jul 2008

I am planning to upgrade to to the latest available SSL version

I want to know what are the dependencies that are available at the system level , does it makes any issues on the applications that are used in this server i,e compatibility problem

If I didn't updated the openssl version , what are the serious security bugs I am gonna encounter ?