Princess Mononoke is an amazing film that everyone should watch. Unfortunately, like most studio Ghibli films, it's very hard to find anywhere to watch this film online legally. So If you want to watch Princess Mononoke online, and you don't want to go down the illegal route, then feel try some of these options:
Xfinity Stream (Comcast)
If you haven't heard of Xfinity Stream before, it's a streaming platform owned by Comcast, so it's totally legal and actually has a pretty good collection of films and tv shows - including Princess Mononoke. So if you want to watch this Hayao Miyazaki film in good quality online, then Xfinity Stream is a good place to start.
There is a YouTuber called Sads who has a "Let's Watch" series on YouTube where he watches Studio Ghibli films, and you can see part of the film as he watches it. Now be warned, you can only see a small amount of the film, so it is less watching the film and more listening to it. If you're already seen Princess Mononoke then you might find this to be perfectly adequate as you'll be able to fill in the blanks. However if it's your first time watching Princess Mononoke, then go for something else!
Disney Streaming Service (TBA)
Although this hasn't been 100% confirmed, it is very likely that the new Disney streaming service called Disney+ will have Princess Mononoke available to watch online, so that will make it much easier for fans to watch the film. The new service will be available at the end of 2019 so keep your eyes peeled!
This is the trailer for Princess Mononoke, enjoy!