At the moment the answer is "None" - with two exceptions:
These are already worthless because the US has shut down our LORAN chains.
They are jokingly referred to as "IFR-Certified Lead Bricks".
The FAA is killing off NDBs one by one - an ADF is basically an expensive, drag-producing AM Radio in many parts of the country, and its utility is in steady decline.
Other than that the core IFR technologies are pretty much sticking around:
VOR/LOC/ILS isn't going anywhere.
Some VORs are getting decommissioned, but even the bleakest plans call for the FAA to maintain a "minimal operational network" of VORs as a backup in the event of trouble with the GPS satellites..
DME is sticking around.
Lots of planes flying around use DME still, and there are lots of DME approaches which serve as good backups for GPS approaches.
(WAAS) GPS is the current "best technology" & isn't going away soon.
The FAA LOVES WAAS GPS. It lets them get ILS-type approaches to pretty much any runway without expensive ground equipment to install/maintain/test. If you have an IFR-Certified WAAS GPS in your aircraft you're on the cutting edge of IFR navigation equipment, even if the GPS itself is older-generation technology (such as the popular Garmin 430W).
If your GPS is not WAAS capable it's still going to be usable, but it's much more limited. It may also pose some problems for you down the road (see below).
Some equipment regulations are changing (as part of the ADS-B Out mandate coming in 2020), but that's not an IFR-specific thing.
The crux of the ADS-B Out mandate is if you want to fly in airspace where a Mode C transponder is currently required you will need two things in your aircraft (if they're not already installed):
An ADS-B Out transmitter to broadcast your position.
This can be achieved in two ways:
A Mode S transponder with Extended Squitter (1090ES); or
A 987MHz Universal Access Transceiver (UAT)
A suitably accurate position source to talk to the transmitter.
Currently that means a WAAS GPS - either a panel-mounted device or a separate "blind" box.
The cost of complying with this mandate falls somewhere within a wide range: If you want a modern WAAS GPS with a touchscreen interface that will let you fly GPS approaches and a new transponder to do the broadcasting part you're going to spend a lot more money than if you install a Universal Access Transceiver and blind GPS source that do the absolute minimum required to comply.