(v.)When someone surreptitiously reads something (usually over your shoulder) without your consent. This can be an email, text message, letter, newspaper etc.
(noun: eavesreader)
I got this funny email from Migs, but I couldn't read it because Julie was eavesreading behind me.
"Just heard the weirdest eavesdroplet"
"Yeah? What was it?"
"Walked past these two guys, and I heard one of them say '...but the lollypop was stuck, and the dog wouldn't stop yelping"