The best way is to wrap Try / Catch blocks around the methods in the service you can afford to let throw exceptions.
However, there may be serious exceptions thrown that should result in the service being stopped immediately. Don't ignore these! In these cases, handle the exception, log it, email it and then rethrow it. That way you will be informed that the exception has occurred and will know what went wrong. You can then fix the problem and re-start the service manually.
Just ignoring it could cause a major failure in your system which you would not know about. It could also be very expensive on CPU/RAM if the service stops then restarts then stops ad infinitum.