Basicly its all RNAV now (doesn't have to be GPS). Even when we fly VOR or NDB approaches we do it via database points and do not even need to monitor raw data (provided two independent FMC are installed), however i think it is still good airmanship to do so, after all i just need to press one button to see it on the screen anyway.
I haven't used any VOR or NDB really in the last few years, however in our old 737 classics we had to check NDBs in russia where we lost ANP over time due to the lack of DME stations, in those birds RNAV was done without any GPS mainly with automatic DME/DME updating. They're gone now and in the NG its dual GPS and usual ANP values hovering around 0.02 to 0.04 NM.