Probably two come to mind real quick, since are the most common ones.
One will be to quote you a flat rate and do not use meter, and normally the rate quoted is 1.5 to 2 times the actual rate for the ride.  Never fall for it, just look for another taxi driver.
And the second one will be that thinking that you are a foreigner and you are not familiar with the city, they will take you on a circular route instead of a straight one, and that can also increase the fare pretty quick.

There are others, like sticking behind a public bus instead of passing it when it stops, to allow the meter to run on time, or control speed to stop at traffic lights when they change to red.

those scams not just for foreigner, chinese also. especially in every city train station. the things worst. those black taxi driver woould ask several times price than usually, no  receipt or give you fake one. take you a circular route. —— so,enjoy you journey.

by the way: be careful in spring festival transport term,that is real a disaster for whole people.

I have only ever been cheated in Shanghai where I took a taxi that I did not realize was a rogue taxi.  The driver charged me for the ride and not per the meter and a 20 RMB trip became a 100 RMB trip.  The proverbial story about the small town guy in a large city.

Otherwise, the most frequent scam that I have found with taxi drivers is that if you give them a 100 RMB or 50 RMB bill for a lesser fare, now and then the driver will try to stiff you wit a counterfeit note.  That has happened to me maybe twice in my years in China, again both times in Shanghai.

Some of the scams that I know of that taxi drivers try to pull in China are going the long way. By going the long way they can get some extra cash instead of if they went the shortest route possible. These are legal taxi cabs. For the illegal cabs they charge you more than if you were to travel by a regular taxi cab so I try to ride the regular cab or use another mode of transportation.

You got the not  using the meter and talking the long way.

Also if you give them a big bill, they'll palm it, switch it for a fake one and then start claiming you were trying to pay with fake money and demand you pay with a different bill.

One expat I know landing on a really late flight and when she took a taxi, he stopped down a back alley and refused to go unless she gave him money.  She just took the role of stubborn, stupid foreigner pretending she didn't understand a word he was saying and just refusing to get out of his cab.  He eventually gave up and took her the rest of the way.

Not a straight out scam, but certainly something to be aware of, is the 'legitimate' taxis at airport, train or bus stations... they prefer to ask where you're going, hustle you, and go for a fixed quote price (which is at least double the real rate). At least with the black taxis, you know it's going to be a rip-off, but it's pretty annoying when it's the real taxis.

The way around that, though, is just to go to the taxi rank, and get them from there - and ensure the meter is turned on - no haggling, no arguing, not quoting. If they refuse, find another taxi. Patience is a virtue!

It used to be the meter that got up surprisingly fast. Now, it's more about taking extremely long roads, but if you know the road it's about slowing down when coming close to a red light, taking the slowest lane, or claiming your way is too slow and taking a road with traffic.
But the worst of all, which happened to me twice and really got me mad, is: you give the driver a 100. He takes it, acts as if he's looking at it (while hiding it from you), then gives you a counterfeit bill that's missing a corner piece, and claims that you gave him a bad one, and asks you to change it. The first time I got extremely lucky because I only had 103 kuai, so he just took the 3 kuai, gave me a fake bill, and drove away. I bought cigarettes with that 100 right afterwards, so I really paid a taxi 3 kuai. The 2nd time, another one tried to pull the same shit with me, but I told him I knew he switched the bills and gave me a fake one (it was horribly made, both appearance and texture. It was like he made it with a computer printer). He said "no that's the one you gave me", I insisted and told him I fucking knew that scam, but, like most locals, wouldn't admit he was wrong (because admitting you are lying makes you lose face, but lying doesn't). After 15 minutes yelling in his idiotic, lying face I gave up, since I was late, and swore revenge.