As mentioned by others, a paid service can help you if you have a dynamic IP which may be helpful for a small business, but there are also several other benefits that I have not seen listed here. One of the primary benefits of a paid service is the length of the TTL you are allowed to set. If you look at GoDaddy for example they typically allow a TTL of no shorter than 30 mins, with a default of 1hour. This is pretty good for general use, but if for example you work for an online university and need to make sure that switching to the new website will be complete worldwide within roughly 5 minutes (like I do), then GoDaddy probably isn't the service for you.
Additionally, most paid services usually have much greater support to prevent DNS hacks including malicious records/redirects but also are better prepared to handle DoS attacks etc. They normally provide much better tracking of how many hits you are receiving and on which DNS names you are receiving those hits. And they also generally provide much more robust reporting on all the things I have mentioned, which isn't hard since GoDaddy provides none.
In short, it depends on your business but if you need your DNS to be up all the time with no exceptions and you have a need to have better/faster control of your records and where your queries are coming from - you will be looking for something more than a GoDaddy and you will be paying for it.