If you're using the Yoast WordPress SEO plugin (which is the best for SEO, in my opinion), and you go under Permalinks within the SEO menu, the first item on the list is the option to "Strip the category base (usually /category/) from the category URL."

If you do this, I would of course first compile a list of your current category URLs and all the URLs that live under them, and drop them into whatever you use for 301 redirects (I use a plugin called Redirection, which is great) and redirect everything on that list to the version of that URL without the /category/.