Until recently, one could view QF award inventory on Expertflyer and this made it much easier to get QF award seats.

Last summer, I was able to get 4 award seats on QF for me and my family (3J, I F) for this summer on the following flights:

JFK-LAX 1 F Award Seat
LAX-MEL 1 F Award Seat
LAX-SYD 3 J Award Seats (on the QF 12, the embargoed flight)
MEL-CNS 1 J Award Seat
SYD-CNS 3 J Award Seats
CNS-AYQ 4 J Award Seats
AYQ-SYD 4 J Award Seats
SYD-HKG 1 F Award Seat, 3 J Award Seats

I subsequently canceled the F award seat an bought an AONE6 ex-MRU instead, but it was very easy.

Now that Expertflyer is no longer able to show QF award space (hopefully only a temporary problem, but I have my doubts), it probably harder in that you won't know availability in advance of calling.

CX used to be easy for me to get one F award seat. In 2003, I got a seat routing SFO-HKG-JNB-HKG-JFK and in 2005, I was able to get a seat for SIN-HKG-LAX (part of a Oneworld Award). I had no luck getting a CX F seat for the trip set-out above from HKG to JFK, LAX, SFO, LHR, CDG or FRA, but was able to get three J award seats for the family on HKG-LAX (the 1 PM departure).

British Airways has been pretty easy for me. I was able to get an F seat from HKG-LHR-YYZ for the trip discussed above and recently got a J award seat for LHR-MRU//CPT-LHR.

Lan used to be easy for F award seats b/w the USA and SCL, but they no longer F on these flights, which is a shame, because the service was wonderful (better than CX, IMO).