I personally find it weird/ugly when a class uses a getter to access its own member data. I know the performance impact is none but I just don't like to see all those method calls. Are there any strong arguments either way, or is it just one of those things that's personal preference and should be left to each coder, or arbitrarily controlled in a coding standard?
Update: I'm meaning simple getters, specifically for a class' non-public members.
Willingness to use getters/setters within class member implementation is the canary in the mine telling that your class is growing unreasonably. It tells that your class is trying to do too many different things, that it serves several purposes where it should serve one instead.
In fact, this is usually encountered when you are using one part of your class to store or access your data, and another part to make operations on it. Maybe you should consider using a standalone class to store and give access to your data, and another one to provide a higher view, with more complex operations with your data.
Protecting a member variable by wrapping its access with get/set functions has its advantages. One day you may wish to make your class thread-safe - and in that instance, you'll thank yourself for using those get/set functions