The only time that it is mandatory to use rel="nofollow" on a link is if the link is sponsored. If somebody paid you for the link, or if the link is part of an exchange, Google might penalize your site for NOT including a rel="nofollow" on it.
You should also apply nofollow to links that are created by your users without review. Otherwise, they have incentive to spam your site.
Besides these two cases, using rel="nofollow" doesn't seem to help you, and might even hurt you.
If all the external links on your site are rel="nofollow" then Google might decide that your site has nothing but paid links. You would appear to be an affiliate and Google's algorithms are not known for being kind to affiliate sites.
Clear external linking may even help. Having relevant external links that are used by your visitors is a sign that you are an authority site. Google has been claiming for years that they want to send more traffic to authority sites.
Five years ago, nofollow might have been able to be used to hoard pagerank for your site. This is no longer the case. Now when you link externally, your site loses pagerank whether or not you use nofollow. The pagerank that is "lost" doesn't actually seem to hurt your rankings as far as I can tell, so linking doesn't seem to hurt.
If you have external links to many different sites, and you are worried about helping one or two competitors that you are linking to, I would consider using nofollow for just those competitors. Don't go overboard with nofollow. Make sure you have plenty of clean external links to balance it out.