For the IR(R), when you won't be in airways, the answer is 'navigation equipment required for the planned route' or something like that. I can't remember the location of the quote but no doubt someone else will. But as things stand, you can't substitute e.g. a GPS (still less a handheld, non approved GPS) for an ADF, for example, although many people use a GPS to 'assist' them on an NDB approach.
Even with a proper IFR approach GPS, there is a gotcha as some approaches have a missed approach based on a conventional navaid which you are therefore required to have. Depressingly often this is an NDB.