Legally there's no such thing as an official authorization to use certain equipment. There is no separate VOR, ILS or PRNAV endorsement/exam or anything like it.
So if you feel confident enough to use a certain bit of kit and it's available, list it. If it's not there, if it's U/S or you have no clue how to work it, don't list it. Simple really.
All this doesn't really matter in a VFR environment. It is supposed to be more relevant in an IFR environment. For instance, if your equipment list does show a VOR+DME but no ILS, ATC is supposed to give you the VOR/DME approach instead of the ILS. If you don't have GPS or any other form of RNAV capability, ATC is not supposed to let you cut corners and navigate DCT to a far-away waypoint which can realistically only be reached with RNAV capability. And so forth.
In practice however ATC ignores the equipment field completely and will give you DCTs to faraway RNAV waypoints, and vectors to the ILS. It's up to you to tell them "unable" if you're not equipped to handle that.
(The only real exception to all this is the VHF radio. Without it you won't get access to controlled airspace, obviously. But as 8.33 frequencies will get more common, you'll find that your flight plan may be rejected if your flight takes you through 8.33 airspace, but you have not indicated the "Y" in the equipment list.)