1) Curiosity 2) Curiousness 3) Nosiness 4) Snoopiness 
• (n.) The quality or state of being inquisitive; the disposition to seek explanation and information; curiosity to learn what is unknown; esp., uncontrolled and impertinent curiosity.
In·quis'i·tive·ness noun The quality or state of being inquisitive; the disposition to seek explanation and information; curiosity to learn what is unknown; esp., uncontrolled and impertinent curiosity. « Mr. Boswell, whose inquisitiveness is seconded by great activity, scrambled in at a ...
inquisitiveness 1. Eager for knowledge. 2. Too curious about other people`s business.