I took a taxi and a 15.60 fare came up, driver pressed a button and a flashing 18.00 came up in Beijing. Why?

Yes, such a bad feeling, right? It probably wasn't the "rip off the foreigner button" though. There is a 1 yuan fuel surcharge per ride, and a surcharge for low speed/idling, which according to the sticker on the taxi says 5 minutes = 1 kilometer, but it's actually calculated every 2.5 minutes. So if your driver was driving slowly/idling for 3 minutes, then you would be charged an extra 0.5 kilometer fare (if not rush hour; in rush hour it becomes 1 kilometer fare for 2.5 minutes) which is 1.2 yuan.

So what happened most likely is you were charged 15.6 + 1.2 + 1 yuan fuel surcharge = 17.80 and then the fare gets rounded to the nearest yuan so 18.