A CPU cooler? Yes. Many CPUS come with one; some do not. You NEED one.
As for additional fans on your case? Probably not. They make extra noise that you probably will not like.
If you have multiple graphics cards, or are overclocking, then yes, more fans are usually better. Just make sure they aid airflow, and not hinder it. Usually front/ bottom to top/back is the way cases are usually set up.