Do today's aircraft still have INS (inertial navigation system)?
Short answer
Aircraft still use inertial navigation systems because INS is autonomous, it doesn't need any external support to work, it provides more information, and is more accurate than a GNSS in the short term. There is no plan to stop using it.
On the contrary, INS is required for certain operations. For instance the B787 cannot be flown without at least one IRU operative. See B787 Master Minimum Equipment List MMEL, item 21-01-01 page 182.
The usual solution for air navigation is to use INS, frequently updated by GNSS to contain drift, as long as GNSS signal is available, accurate and reliable (professional GNSS receivers are able to determine their reliability).

GPS/INS sensors fusion, source

Details
While INS has several disadvantages, namely initial alignment time and drift, it has also unique capabilities:

INS is autonomous, position is determined without external cooperative support.

INS position can be updated 1,000 times per second.

INS provides position information like GNSS, but also orientation (attitude), rotation rate and related accelerations. In the short term these data are very accurate. For example, the yaw damper uses instantaneous motion data to counter Dutch roll.

INS provides True North direction.


On the other hand, global navigation satellite systems (GNSS):

Contrary to inertial navigation systems (INS), are dependent on a lot of factors to work, including space vehicles, ground stations, antennas, or solar activity.

GNSS signals can be obstructed, altered or jammed.

GNSS is updated at a slow rate (e.g. once or 10 times per second, that is by increment larger than 20m for an airliner at Mach .85), due to the heavy computation required to extract and process the weak GNSS radio signal.

The best known GNSS, the American Navstar GPS, is a military system funded and managed by US Air Force.

While GPS is in effect always accurate for civil uses, it must be remembered there is no guarantee from the US DoD on that. The Navstar GPS operational specifications for SPS (civil) service allows for 72 minutes per day (2σ / 95th percentile) with a DOP &gt; 3, that is more than 17m horizontally and 37m vertically. During these 72 minutes, the error is unlimited.


In the field of aviation, GNSS and INS are more and more coupled with air data and magnetometers, that's called data/sensor fusion to take the best of each system, cross check results and detect sensor failure.
As a everyday life example: Without an inertial sensor in a car &quot;GPS receiver&quot; (more accurately: a GPS-aided navigation system), the navigation system would be helpless at roundabouts. The GPS receiver instantaneous precision, its low update frequency, and its lack of orientation sensing would prevent it to correctly derives the actual position and the closest roundabout exit.