So I just picked up my new S3 on the release date and recently have been getting annoying "Severe Weather Alert" texts from Verizon. After getting texts about flash floods 3 hours from me I was getting annoyed. So, I jump online and couldnt find a single thread about it and if I did people were talking about a weather app. I finally figured it out and thought this may help others as well.
hit the menu button
scroll down to emergency alerts
Uncheck the alerts you dont want to receive
Back out of the menus
Viola! No Severe Alert texts!
Unfortunately presidential alerts cant be disabled, but those are probably pretty important anyway.