I get the above error message when I try to run some programs in ssh -X

xterm works fine. But when I do gedit, I get the above error. If I do sudo gedit, then the program runs without the error.

xyes, gnome-calculator, chromium-browser also works. I did a little investigation online, but they usually try to get some X program running. The problem I face is that some programs need me to do sudo in order to make them run. I was wondering why this is required.

EDIT: I killed all gedit on the system, and tried the command again, this time I get:
GConf Error: Failed to contact configuration server; the most common cause is a missing or misconfigured D-Bus session bus daemon. See http://projects.gnome.org/gconf/ for information. (Details - 1: Failed to get connection to session: Error connecting: Connection refused)

Do you have xauth package installed in the machine that runs X server ?

Yes, I do. I have seen approaches that talk about using it, but now that X programs work, I wonder why do only some programs like gedit not work.

Maybe check permission on .Xauthority file

ssh <server>
ls -l .Xauthority

I have the permissions. Besides, I can run other X programs. For some reason gedit won't open.

There must be file permission problem somewhere if you are able to run gedit as root

Try adding this line to /root/.bashrc, replace user with your user name.