How can I run a program remotely via SSH but display locally

Is it possible for me to SSH to another server in Linux (Ubuntu), run a program there but display it locally?

And is it possible for me to SSH to another server in my terminal, and configure it so that all graphical programs (Firefox, Emacs) run in that SSH session will be displayed locally?

By adding the "-Y" flag to the ssh command, the display will automatically be redirected to your local computer.

ssh -Y <remoteip>

Then, if you start Firefox (or any other X application) in that ssh session, it will be displayed locally. (If you have a xserver running locally of course)

You are looking to do remote X. This is a good mini HOWTO.