This app was mentioned in 7 comments, with an average of 1.71 upvotes
there is a NYC taxi app. it's called curb: https://play.google.com/store/apps/details?id=com.ridecharge.android.taximagic&hl=en
been seeing ads for it in yellow taxis for a while now. i was in a taxi the other day and the guy had a tablet mounted in the center that showed available pickups.
There may be multiple that work, but this is the one I've used. Not perfect, and not guaranteed it'll find you a car available, but it's good to have another alternative. https://play.google.com/store/apps/details?id=com.ridecharge.android.taximagic
Beacuse they were competing with each other.
But app developers jumped in. I've used Curb (née TaxiMagic) taking my mom to doctor, and will check out easytaxi.
https://play.google.com/store/apps/details?id=com.ridecharge.android.taximagic&hl=en
https://play.google.com/store/apps/details?id=br.com.easytaxi&hl=en
Curb has been around for a long time. People just don't look
edit:
Ah, found a US nationwide Taxi hailing App (exists in 60 American cities): https://play.google.com/store/apps/details?id=com.ridecharge.android.taximagic
Another US based taxi app (Boston, NYC, Chicago): https://play.google.com/store/apps/details?id=com.goarro.Arro
Found a taxi app for not-US cabs, it looks great for travelers: https://play.google.com/store/apps/details?id=br.com.easytaxi
Another foreign taxi app but its in NYC as well: https://play.google.com/store/apps/details?id=com.gettaxi.android