Exception handling continuing the excecution
How about something like this?

Define a one-method interface like so:

public interface TryAndLogFailure { void execute(); }


Then define a method which takes an object which implements the interface and does your exception handling for you:

public void tryAndLogFailure(TryAndLogFailure talf) {
  try {
    talf.execute();
  } catch (Exception e) {
    logger.log(...);
  }
}


Now your calls to the methods can be sequential:

tryAndLogFailure(new TryAndLogFailure{ public void execute() { methodAAAACanThrowException(); } });
tryAndLogFailure(new TryAndLogFailure{ public void execute() { methodBBBBCanThrowException(); } });
// etc...
tryAndLogFailure(new TryAndLogFailure{ public void execute() { methodZZZZCanThrowException(); } });


Admittedly, this could probably be worked a little more to make it prettier, but this is my first crack off the top of my head. If only Java had support for closures.

(Also - I should note that I agree with Winston. The reason why this code feels ugly is because the concept itself is ugly. Catching Exception is almost never a good idea and requires strong justification. Given more context, we may be able to help you redesign the code to avoid this sort of code smell.)