I have little knowledge about the US state of affairs but I was always under the impression that most of the extended permissions mostly apply to the FBI (warrantless wiretaps, ...) and not to the regular police - hence my cautious wording. I might be flat out wrong with this.

Anyhow, the assertion is still true for germany. Unless there's an emergency they're not allowed to enter your house, ask for anything more than your name (well, they can ask, but you don't have to answer) and so forth. These regulations get ignored on a regular basis, but that's a different matter completely.