The default Xsession on Debian is run with ssh-agent so that ssh connections can be initiated more easily (after you have performed an ssh-add). This is controlled by the file /etc/X11/Xsession.options:
use-ssh-agent
You can have your ssh passphrase asked for each time you log on. Using gdm and the Debian Session (rather than the Gnome Session) will load the /home/kayon/.xsession file which can contain:
#!/bin/sh ssh-add .ssh/id_dsa < /dev/null exec gnome-session
If you have ssh-askpass and ssh-askpass-gnome installed you will be prompted for your passphrase. All connections to hosts which have the public key will now be direct (no password or passphrase required).
By default the ForwardX11 option for ssh is turned off. Thus, when you connect to remote hosts you won't be able to display X Window System applications on your screen. You can turn it on per connection with:
$ ssh -X plymz
Or else you can turn it on for all connections to a particular host by adding the following line to /home/kayon/.ssh/config:
Host plymz ForwardX11 yes
Or even more generally allow X Window System forwarding through all connections:
Host * ForwardX11 yes