The cabs I've used in the last few years have all had credit card swipers in the car. I figured this would be a universal feature of any moderately populated cities' cab system in 2014.
The strategy used in Chicago when a credit card machine isn't working is just to tell them you don't have cash and you're walking out if they won't accept a card ("for a 'broken machine'") Magically it starts working again. [The city of Chicago mandates that they must be able to accept credit cards]
Using the 2013 NYC Taxi data that was posted earlier, the amount of people who pay with cash vs. amount of people who pay with credit card is about 50:50.
Here's a quick spreadsheet of the distribution: https://docs.google.com/spreadsheets/d/1EaP9LJ7i1MPREuypejOr...