Princess Mononoke is a tale all about protecting nature while respecting its ties to technology; a beautiful tale that longs for mutual acceptance by both parties. This tale of war and peace is an incredible Studio Ghibli classic with such a unique story that there's very few to rival it. Of course, we do have some recommendations if you are looking for something else to feast your eyes on.
You can never go wrong watching another Ghibli film such as Spirited Away or Howl's Moving Castle, seeing as they'll have many similar themes with a beautiful way of showing you fantastical lands and whimsical characters. However, if you really want to expand your horizons, we do have other series like Mushishi and Made in Abyss which will show you more of a variety in terms of story. Some are more curious whereas others are dark and terrifying. What they all have in common is that they're all excellent anime that you can't go wrong with watching.
Let us know which ones you chose to watch and vote up your favorite recommendations for anime like Princess Mononoke!