Actually, being able to traverse a person's land to gain access to a location on the other side is still alive and well. Most notably, for beach access .. and all can traverse the land, not just the police. These exceptions are generally carved our by law (eliminating the common law) or by court order.
If the police can enter w/o a warrant to stop the destruction of evidence is another exception.
The police do not have mystical powers; they are subject to the limitations of a notice like any other.
If they wish to violate a notice then they'll need some prior law to support the violation otherwise they too are committing a criminal act.
Can they come and knock on your door w/o you having been involved or suspected of being involved in a crime (like they saw some activity on your neighbor's property) then answer is likely no. They can send you a letter, call you etc. You have no duty to assist the police so they have no right to ask (IMO).
We still have rights as property owners and one of those is to control who can be on your land...this includes controlling anyone. Some laws may carve out exceptions. Its up to the landowner to know what they are.
But there is nothing wrong with filing a notice ... anyone comes on, then call the police. If it is a policeman, then you calling the police telling them to remove the cop or ask for his arrest is completely appropriate.
If there is an exception or a claim of exception, the police on the phone will tell you ... and you can check it out...and if not true, still followup later.
You don't have to answer your door either...I have had cops knocking and I just let them knock until they go away. I always say: let them knock down the door...then you'll have evidence it was a forceful entry.
Google scholar is a resource for folks to use
ex for WA, notices are still alive in this state, as in most:
http://scholar.google.com/scholar_c...3440&q="notice+of+trespass"&hl=en&as_sdt=4,48
And a good case talking in more detail about trespass signs, discussing curtilage in WA:
http://scholar.google.com/scholar_c...9579&q="notice+of+trespass"&hl=en&as_sdt=4,48
A notice of trespass has more of a legal effect than signage IMO...I have seen cases of people entering driveways when issued a notice and they were found guilty. This closes off curtilage areas whereas signs do not.