Is there a verb meaning watching others' phone / read a newspaper stealthily (i.e. without their noticing)? E.g. while sitting beside someone in a subway and checking what he is doing.
I'm looking for a verb for this act which has some negative connotation.
Shoulder surfing has a negative connotation.
Wikipedia says:
In computer security, shoulder surfing refers to using direct observation techniques, such as looking over someone's shoulder, to get information. It is commonly used to obtain passwords, PINs, security codes, and similar data.
You are reading over their shoulder, even if it doesn't actually involve reading over their shoulder because they are sitting next to you on the train. "Over someone's shoulder" is a set phrase. It has the negative connotation of a surreptitious act.
OED includes shoulder surfing, for example "The librarian wouldn't punch in the ID and passwords if you were looking over her shoulder, trying to shoulder-surf," (my emphasis) but as Chenmunka comments on the question, it's normally used for [and the OED defines it as] "the practice of surreptitiously watching a person who is using a computer, cashpoint machine, etc., in order to obtain confidential information, such as a password or personal identification number, for fraudulent purposes." Note that even that doesn't actually have to be physically looking over someone's shoulder, merely being positioned to view the information.
Had you asked for an adjective, I might have gone with surreptitious, but since you want a verb, I suggest snoop, as given in Merriam-Webster:
to look or pry especially in a sneaking or meddlesome manner
As example uses that fit your descriptions:
"Hey buddy, quit trying to snoop! Buy your own paper."
The police determined that the hackers were able to obtain some users' information via snooping their activities at public wi-fi hotspots.
The other day at the airport, I caught someone snooping at my text conversation. How rude!
eavesdrop: To listen secretly to what other people are saying. (M-W).
My suggestion covers the OP's stated context of a phone but not that of a newspaper. The action of eavesdropping on someone's phone conversation (listening to or trying to listen) carries the OP's requirement of a "negative connotation". However, I am unsure of any broader meaning the OP intended here, perhaps going beyond the ordinary meaning of the words "looking" and "watching" to include listening to someone's phone conversation in a "subway" where fellow passengers in proximity have little or no choice but to "watch/look" and listen.
