This app was mentioned in 1 comment, with an average of 2.00 upvotes
I've used an app called cab4me that is free and finds a nearby cab service.
https://play.google.com/store/apps/details?id=com.cab4me.android
But to be honest I notice the quickest response time with Uber. And with the Uber app you can actually track the car as it's driving towards you.