Stop

1) "Stop reading" - the reading stops
2) "Stop to have a coffee" - I stopped because I wanted to have a coffee

1) In the first case we stop the action that follows.
2) In the second case we stop something else, for example working, in order to complete the action that follows. Here "to" introduces a purpose and is short for "in order to".

Examples:
1) She stopped calling him after that argument. (She never called him again.)
The computer stopped working, I need some help. (It does not work anymore.)
2) I tried to concentrate but the phone kept ringing and I constantly stopped to pick it up. (Every time the phone rang, I stopped working and picked up/)
We need to stop to get some petrol. (We are driving now but we need petrol, so we should stop and get some.)