The answer is simple, they shouldn't be allowed to do that, but they are powerful enough to do it anyway.

What right do they have to keep charging you after you have contacted them to let them know that you want to cancel?

We are discussing cable companies and phone companies, not retailers.

Which store acts like this?

It is totally wrong that these companies have so much power over their customers.

Just like you can order the service online, you should be able to cancel the service online.

Some of these companies make it hard for people to switch by making them stay on the phone for hours. Shouldn't the customer's stating that he or she wants to cancel be enough to cancel? Why is the company allowed to drive the customer crazy?