Can you turn Airplane Mode off after you land or finish taxiing on a plane? I have seen some turn it off after landing and some after taxiing and I have never heard an official rule stating which one is correct.
There are two ways of looking at this. The physical 'can you' and the legal.
From the physical, every single transmitting device on a plane has to be certified to legally fly on the plane in transmitting mode. Most devices 'probably' won't interfere, but even adding a wifi router onboard takes hours of testing, compliance, and certification (source: I was on the Qantas wifi programme team). Since they can't possibly certify every single variant of mobile phone, it's easier to just say 'turn it to airplane mode'.
From a legal point, If you forget, or don't bother (and our scanners could see this happening on almost every flight), it almost certainly won't make a difference, but you are technically transmitting onboard an aircraft with a non-certified/compliant device, which is illegal in many countries.
You're also meant to legally always follow instructions of the flight staff. They might seem like just friendly hosties, but there are serious consequences available in most countries for disobeying instructions of the flight crew.
So if you're told to keep it off, and they forget to tell you it's ok, technically you shouldn't be turning it on again until you disembark (usually into the terminal). Again, it almost certainly won't do anything bad, but you asked 'can you' vs 'should you' so I'm trying to cover both.
Easy option: It's a few min of peace of quiet from your phone and the outside world. Enjoy it :)
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.