My Verizon Galaxy S4 started doing the same thing last month. It's extremely random...maybe twice a day, sometimes 4-5 times within 10 seconds! I went to Application Manager and unchecked the Notification box in every downloaded app...it still happened. Verizon store told me to contact Verizon support; I did and was escalated to 2nd tier. Everyone claims no knowledge of this, yet it's all over the internet. Finally, one tech contacts Samsung and finds that they are aware of some S4's and Note 3's with this problem. I'm told it's a corrupt Android OS and resetting to factory default only re-installs the corrupt OS. I need to go to the Samsung desk at a Best Buy where they can "scrub" my phone and install a new OS or I can get a new (refurb) replacement with a new OS. I got a new replacement, reinstalled all my apps, unchecked all notifications and IT STILL HAPPENS!!!
I installed an app called "Notification History" which gives a log of all notifications I've received. The strange thing is that these "phantom" notifications never display the flashing blue LED like I got a text , IM or message. Nothing ever appears in the Notification Bar and the Notification History app doesn't show any notification that caused the sound to go off. I'm getting really irritated by this going off in the middle of the night, in the middle of phone calls and during meetings!