Using cascading menus (a.k.a. multi-level menus) is still a very common design pattern, but using 3 levels of nesting should generally be avoided, so you may want to consider using mega-menus.
It sounds like you're planning on having 3 nested menus, which goes against recommendations from both Apple and Google (as pointed out by @Mike M). A primary UX issue with cascading menus that activate on hover, as pointed out in @Ken Mohnkern's answer, is the narrow path for the mouse (sometimes called a narrow mouse corridor). There was an excellent discussion a few days ago that discusses this exact issue, and there are some additional resources there that may be of interest to you if you choose to use cascading menus.
Without knowing more about your information architecture, page layout, and other planned navigation, it's hard to make a concrete recommendation, but I suggest considering using mega menus. The NNGroup has shown that mega menus work well for site navigation. One of the big advantages of mega menus is that they allow you to show more information at a glance. Let's look at Amazon's top level navigation:
As you can see, it's a cascading menu, however, the only submenu is a mega menu. Things to note:
- The top level menu clearly labelled what was going to appear in the submenu (Health, Beauty, & Grocery)
- The submenu is a mega menu that contains two categories (Health & Beauty, and Grocery).
- They used the mega menu to market their instant coupons using great typography and an attractive image. Unlike traditional cascading menus, mega menus afford the opportunity to add in additional design elements that can be used to market or promote related content.
When viewed on mobile, the menu is no longer presented as a mega menu, but a more common dropdown:
If you do go with cascading menus, Smashing Magazine has an article on best practices for dropdown menu design. The article is from 2009, but contains some good advice which is still applicable. They have a more contemporary article which offers good practical advice on interaction design related to dropdown/cascading navigation. Design Modo also has an article on UX Design Tips for Dropdown Menus with more practical advice.