What is the correct phraseology for declaring a fuel emergency?
(This is very closely related to this question, and see this one too.)

At least in the US, cutting into fuel reserves isn't an emergency by itself. But assuming that things have gone beyond "minimum fuel" and you clearly need priority for landing then you should indeed declare an emergency.

The wording you mentioned seems 'weak' to me; if you do have to declare an emergency, there should be no possible doubt about it or about what you need. Assuming that I was already in contact with ATC, I'd probably say something like this (see the AIM 6-3-2):


  Mayday, mayday, mayday. Louisville Approach, N12345 is declaring an emergency, low fuel. We are now direct runway 35R for landing. 3 on board, 15 minutes fuel remaining.


Note that if time is critical I'm not going to "request" anything, I'll just tell ATC what I'm doing and let them sort out the rest. That phraseology and statement of intentions should be understood anywhere in the world.