Can you turn Airplane Mode off after you land or finish taxiing?

The effect of leaving Airplane Mode off: your phone will be trying to connect, using maximum battery power, to any phone company cell it can ping during the flight. The connection is guaranteed to fail since at airplane speeds you will be out of that cell's range before a successful handshake is concluded—or at least before significant amounts of data are sent or received. You won't be happy because of battery drain. The phone company won't be happy because any cell that receives your attempt to connect (that's not impossible over several miles with no buildings to interfere) will be attempting to locate your now-far-away phone to hand over to another cell, at maximum signal strength and power; plus, of course, you are briefly using a slot that could be available for another user who won't be miles away by the end of the opening handshake.

I know there are stories that your cellphone can somehow interfere with the plane's navigational system, but that's not the case.

Once you have landed, and are taxiing to the gate, you can establish a successful connection and use your phone just you would leaving the airport in a car. (This supposes cell coverage in the airport vicinity, which is a given at any major city.) This doesn't answer any question about legal regulations, which vary from one country and airline to another, but explains the physics.

On all flights I have taken in the past couple of years, this information was either available in the airline’s information leaflets in the seatback pocket or it was announced when we landed – or both. I cannot remember a flight I took recently where the passengers were asked to keep their handheld devices in flight mode until the aircraft came to a complete stop; they all had some sort of do what you want after touchdown.

My experience is limited to flights in Europe, East Asia and between those two. Legal standards may differ.

Actually, in Europe you can have your phone or any other device throughout the flight without Airplane Mode enabled. EASA (European Union Aviation Safety Agency) gave permission for that almost 5 years ago)

But it is the airline company's final decision.

As others have said, this will depend on country and airline. That said, in the US, immediately after the wheels touch the ground, I quickly turn off my Airplane mode as my phone will shortly be able to get cell signal for 4G. A few seconds later, attendants have explicitly said that although passengers should stay seated, they can turn off Airplane mode and surf the web as they please. Makes sense since after landing, it should be smooth for the most part getting from the runway to the gate.