When you are installing a program using .deb packages on Ubuntu, you can check dependencies of package using Ubuntu Packages Search. For example I can see dependencies of Wireshark from here. As you can see, dependencies marked by red bullet. If you know all packages your program depends them, you can download and install them using dpkg.
Is there any alternative website for RPM packages? Specially for RHEL?
I know that I can get these packages' names by other methods such as when installing RPM package using rpm -i, but it is not user friendly and needs access to running Linux.
In fact that's not a one but four different questions :).
*) First you can quickly list a downloaded package's dependencies/requirements by using the following commands:
$ rpm -qp mypackage.rpm --provides
$ rpm -qp mypackage.rpm --requires
*) Second, you can use yum utility in order to satisfy these (somewhat cryptic) dependencies automatically (assuming that all your repositories are set up correctly, and all the dependencies are available):
$ sudo yum install mypackage.rpm
*) Third, there are several RPM search resources, some of them already suggested above. I'd like to list another one, just for the reference - pkgs.org.
*) Fourth, there is an additional popular repository for RHEL5 and RHEL6 distros - EPEL. Note that it's not supported by Red Hat.
Hope my answer(s) will help.