In both the 2002-2007 Spider-Man trilogy and the newer Amazing Spider-Man trilogy, Peter Parker is seen stalking his love interest (Mary Jane and Gwen Stacy, respectively) to an unhealthy degree.
Was this present in the Spider-Man comics as well?
Yes. He often surprised them by showing up out of nowhere.
Of course, stealth is his modus operandi. He often spies on bad guys, either to take pictures for the Daily Bugle, or to be able to beat them as Spider-Man. This seems to have become second nature to him, carrying over into his private life.
I remember him secretly snapping pictures of Mary Jane. (I'll see if I can find an example).