How do you get a mine cart to stop by itself with out you being there with..

You do not need to say what version you are asking about because you are asking you question in the Xbox version's Q&A, therefore you are asking the question for the Xbox version.

There are three easy ways.

First, have it hit something. Put a block at the end of the track and it will stop dead upon hitting it. A dropped item or mob on the track will also stope the minecart.

Let it roll to a stop. This takes some calculations, and takes to long. I include this just to be thorough.

Put an unpowered power rail where you want it to stop. When a minecart passes over a powered power rail, the cart speeds up, but when a minecart passes over an unpowered power rail the minecart will stop dead. By playing with switches and redstone, you can turn this stop on and off as you pass by. This is my favorite option, because you don't need to make multiple tracks connecting every possible stop, only multiple stops along one track (no switching carts needed).

Put down some redstone track and don't activate it. It works like a brake.