EdFred
Taxi to Parking
For flight following, I agree - Though rather than just a callsign or callsign plus the extraneous "request", I'd say "<Facility>, <callsign> request traffic advisories." That way if they're too busy they can say "unable" without needing an extra exchange.
I make this call often:
"Madison Approach, Diamond Star 569DS, Juneau, 4,500, landing with XRay." Gets the necessary information across as efficiently as possible. If I'm flying in (and call in as, you smartasses) the 182, I never get a request for further information. I have a couple of times in the DA40, usually a request for "Say aircraft type?" because we're the only Diamond Star based on the field, we haven't had that plane very long, and they're unfamiliar with it.
I do make sure to say it clearly and without going too fast at the beginning, which gives the controller a chance to pick up their pen while I'm still on "Madison Approach..." and take down the request. It may make people feel cool to rattle things off as quickly as they can, but better communication occurs when fewer words are used rather than less time per word - Speak at a moderate pace and get rid of the extraneous words.
I've also gotten it when landing at the facility. So now it's just "(Facilty) (Callsign)" on the first one.