Where should I put my ajax call if I want to get some data from an external link or website? Should I put it in the controller, or in the service?
You should try to keep your controllers as "thin" as possible. That is, they should call other classes, which do the actual work.
The Craft approach is to keep most of your code in service classes, and if you're just starting out with plugin development, I recommend you follow this pattern.
Bear in mind, though, that your service classes define your plugin's API.
In other words, if you add a public method to one of your plugin service classes, you're essentially telling everyone "hey, you can use this method if you like".
If you're interested, I wrote a blog post about this a while back.
In summary, keeping your code in services is much better than keeping it in controllers, but don't treat your service classes as a dumping ground for everything.