Rakuten Viki is a popular source to watch modern Asian TV dramas, including from China and Taiwan. Some content is behind a paywall, but there are still tons of good shows available to watch for free with ads. It also has a "learn mode," which allows users to see subtitles in both the target language and another language, and to gloss over words to see their definitions quickly.
There are also several popular TV dramas that are freely and legally available on YouTube.
Graded Watching: this website lists several Chinese TV shows with information about genre, country, and even vocabulary lists to go with the series.
Academic Video Online: a video database which provides access to short videos and movies in many languages. By clicking "Filter," you can narrow the language. It lists all three categories "Chinese," "Mandarin," and "Cantonese," so you may have to look through multiple categories to see all of your options.
Kanopy: another video database with some Chinese movies and movies about China. WashU buys individual titles on Kanopy based on student requests. You can watch or request a title on Kanopy by clicking "Watch Now," and then "Find Your University." If this title has not been purchased by WashU, it will ask you to fill out a request form explaining your need for the content.
The Chinese Film Project: an open-source project that aims to make classic Chinese movies more accessible. If you are interested in older movies, it is a great resource to learn about the most influential Chinese movies. They provide over twenty movies with English subtitles as well as a free, self-paced movie course. Their content is also available on the Modern Chinese Cultural Studies YouTube channel
Click here to see the full list. It should say in the record whether or not there are English subtitles. Keep in mind that this list may include movies in Mandarin, Cantonese, or possibly other languages if some Chinese is spoken in the film. Below are recommendations of influential and iconic Chinese films: