iPhone 4 makes random text sound

My iPhone 4 makes the text alert sound (or just vibrates if I have it on vibrate) for no reason about once or more a day. I have all push alerts turned off and, just in case, I check each time to see if my email or other apps using push alerts have something new when it makes the sound.

I recently got a refurbished phone after having cracked the one in question and this refurbished one does the same thing. So two different phones that have been through multiple software updates and have push alerts turned off still randomly make text message/email alert sounds.

Anyone know what's up?