Are you allowed to uncover a person's private information by searching the internet?
Says R. Asher Meir, the Jewish Ethicist:
One area is the prohibition on idle gossip. The Torah teaches: "Don't go as a talebearer among your people" (Leviticus 19:16). Rashi's commentary explains that a talebearer (in Hebrew 'roche'l) is like a spy ('rogel') who goes from house to house hearing what gossip is told about someone and then spreading it about. The information is all known, but the forbidden talebearer puts it all in one place and disseminates it. Jewish law states that gratuitous gossip about personal details is forbidden even if the information itself is not derogatory, since people don't want to have all their private information made public. (1)I have to admit that I don't see his last point. It seems a bit farfetched to me to extrapolate from guarding the visual privacy in one's own home to protecting one's personal but public information.
Another area is privacy among neighbors. The Talmud states that "Loss of privacy (literally, damage through seeing) is a kind of damage." (2) The consequence of this law is that neighbors can be compelled to pay for partitions to keep them from viewing a neighbor's courtyard. Even when the protected area is one that is visible to passers-by, the neighbor's ability to see is a greater invasion of privacy, since the neighbor sees constantly. (3)
These sources can be readily extrapolated to the case of web searches. In both cases, there is a distinction between casual and legitimate observation of public information, as in a aside in conversation or a person's activities viewed in passing by a stranger, and the forbidden practice of deliberate efforts to concentrate and disseminate information, for example by a habitual gossip or a neighbor who observes someone constantly.
In the case of web searches, it would be permissible to do a simple web search of someone's name, to see some of their most prominent activities. This is today's equivalent of a simple inquiry to a mutual friend, without deliberate prying into details beyond what is easily available...
However, this is different than making a concerted effort to uncover all available public information about somebody. For example, information garnered from a simple search could be used to identify other sites where information is posted but blocked from search engines, or to identify web aliases that a person uses to intentionally hide their identity in internet communications. This would be forbidden in the case of a private individual. But it is a legitimate and widely used practice to find information about a business, since a business must assume that competitors will seek any publicly available information and take responsibility for controlling such information.