FAA has published an update to the AIM, effective 26 May 2016, and it includes a big change if you have an IFR-approved GPS [i.e., a “suitable navigation system” as defined in AC 20-138 and AIM 1-2-3 (b).]
Now, if you fly a conventional approach based on a VOR or NDB (but not a localizer), you can fly the procedure entirely with the GPS, provided you can monitor (using a separate CDI or a bearing pointer) the VOR or NDB facility specified for the approach.
The new language is in section 1−2−3. Use of Suitable Area Navigation (RNAV) Systems on Conventional Procedures and Routes.
The summary of changes to this AIM update notes that:
This change allows for the use of a suitable RNAV system as a means to navigate on the final approach segment of an instrument approach procedure (IAP) based on a VOR, TACAN, or NDB signal. The underlying NAVAID must be operational and monitored for the final segment course alignment.
The new text in the AIM is in paragraph 5 of AIM 1-2-3:
5. Use of a suitable RNAV system as a means to navigate on the final approach segment of an instrument approach procedure based on a VOR, TACAN or NDB signal, is allowable. The underlying NAVAID must be operational and the NAVAID monitored for final segment course alignment.