The Internet cannot be expected to remain a place where one is free from surveillance and consequences due to illegal behavior. With more people online, it only reasons to follow that more crime is online now, too. While I don't think police should be given carte blanche access to online information, I do think that a court order of little difficulty in obtaining should be permitted to retrieve it for investigations.
They should because sometimes they're needing to find a criminal and that criminal could be hiding out with someone else well when they check their facebook or email or what their IP address is logged which would make it a ton easier to get the criminal off the street.
Yes, police should have access to any and all incriminating evidence of criminal activity, but like all else, only with probably cause and with a properly received search warrant. Certain crimes may never be stopped or prevented, such as child pornography, without the ability to ascertain what websites, images, and correspondences individuals may have had online. As long as the police follow the rules themselves, then it is a simple logical idea that if someone does something illegal online then it may be incriminating and used against you.
The police should have access to the information they need to do their jobs, but only by following the proper channels. They should not be able to get anything they want without any judicial supervision, and they certainly should not be allowed to go on a fishing expedition. So, I think they should be given access, but not freely, and certainly not without third-party supervision.
The police shouldn't have access to someone's information from their internet provider. The users have a freedom to use the internet as they please and their usage should be private. If a user is using the internet for illegal uses it should be the internet provider's responsibility to halt the usage of the user and not get the police involved.
The police should never have access to our information by our internet provider! The police should not know our personal or private information unless it's necessary to prevent a crime from actually occurring. Even then, the police must have just cause to get that information, and not be allowed to get it because of hearsay or mere suspicion.