Calling US controllers
 

In the UK, entry to Class D airspace (usually but not always from Class G) requires a positive clearance from the controller but it is commonly said in aviation forums in the UK that in the USA no clearance is required to enter Class D, the pilot only has to establsh 2 way contact.
Is this correct or do US controlling authorities require other information such as position, heading, altitude etc?

All you need is 2-way communications with ATC which needs to be mainteined for the duration of flight within said airspace, according to the FAA.

The same is true for Class C in the USA. Radio contact.

And that is for class C and D in the US. For class B you need the explicit clearance "cleared into the Bravo".
It makes flying in those busy airspaces so much easier.

ICAO doesn't differentiate between IFR and VFR fligths when it comes to a clearance.

So technically you're subject to ATC, and thereby need a "normal" clearance when flying VFR.... you know, cleared to... via.... level... etc. According to ICAO that is.

But some countries just handles it a bit different and only provide "instructions" for VFR flights and leave out the "cleared".