A lot of people don't seem to know about it, and think they HAVE to root in order to remove bloatware, and considering the Galaxy S4 is on AT&T and made by Samsung, there's bloatware GALORE on this thing.
A quick run through...
Open up "Settings" from your "Apps" menu, hit the "More" tab in the top right hand corner, and select "Applications manager." From here, you'll find 3 sections, "DOWNLOADED" "RUNNING" and "ALL" (you may have to tap running in order to have the selector move to where all is visible). Select "ALL" and find the program you want gone, select it, and in place of the "uninstall" button you'll see a button saying "disable." Click this button (if it asks to uninstall updates, do so, and press the disable button again) and enjoy that one annoying program showing up in your apps list no longer being there. As added good measure, I also force stop the program.
Keep in mind, there are system level processes listed here, that if you disable, your phone may freak out. ONLY DO THIS WITH ITEMS YOU KNOW YOUR PHONE CAN DO WITHOUT.
I AM NOT RESPONSIBLE FOR YOU DISABLING SOMETHING THAT RENDERS YOUR PHONE INOPPERABLE.
*edit* This is not a COMPLETE removal. It DOES remove the application icon from your apps list, and I have not had any update notifications or any push messages from a disabled app. They will still show up in the "ALL" listing of the Application manager at the very bottom saying "Disabled." You can also uncheck the "Show Notifications" box to ensure that no notifications are sent from that application as an extra annoyance-killing measure.
A poster had a question about background services: