I usually apply the common sense route which isn't neccessarily the one we are taught.
If, as happenned recently, a pilot calls "London we have a medical emergency, request priority landing at destination" I will reply "Roger, PAN acknowledged, route direct..." as the words "emergency" and "priority landing" are quite blatent.
However I will ask if a pilot is declaring an emergency, maybe with explaination that priority will not be affected if none declared, in a situation which is still very common whereby at the end of the initial call the words "..and be advised we have a medical emergency" are added.
As has been previously said, if someone says "we have lost all power to all engines" I won't even ask "are you declaring an emergency" as its self evident.
Basically I choose what to say on what I am initially told, but it does make it so much easier and less naucious if the correct words/phraseology is applied within the initial call.
When priority is affected by ATC then the controller who initiates the priority has to fill in paperwork which is forwarded to Investigations, so trying to avoid the phrase (and subsequent form filling) only delays the paperwork for a few weeks. I know how we all try to avoid it, but its still part of our job on both sides.