End-to-End application testing from a users standpoint

I am looking for a good way to consistently test my web applications from the end users point of view. I have all kinds of ways to check to make sure my code is working behind the scenes. I can’t count the number of times that I make a change to a piece of code, test it and it works fine and then deploy it only to have it blow up somewhere else weeks later. I have by that time forgotten the change I made that caused it to blow up. I need something that I can run every time I make a change to assure me I did not break something somewhere else.