Ubuntu only opens the minimal gnome stuff at login and boot only activates a login shell. You will have to be more specific - what is opening that you want to shut down? Give examples?
If applications are starting as you have left them before - (say, you last logged out while firefox window was still open so whenever you log back in again, firefox starts up) then you need to close everything before you logout.
If you don't want ubuntu to remember your open windows, try
system > settings > sessions and uncheck the "remember session changes" box.
There are also tabs in the sessions dialog which let you control what processes start when you login.
Also look in system > administration > services
Your control over what runs and what doesn't tends to be much more coarse than with redhat or fedora. However - ubuntu comes with a minimal set of apps, and only the bare minimum needed are started at boot.
Since you are new to ubuntu, have a look at:
http://easylinux.info/wiki/Ubuntu:Edgy
... this will help you configure your system, just resist using any of those automatic scripts like automatix or easyubuntu.
