There were audio and film recordings of the IMT, but the problem is the trials were both long and multilingual. As such, the digitization of the film portions online is quite limited. The Robert H. Jackson center has Jackson's opening statement which is a combination of film, infographics, and photo stills edited by CourtTV (the link is Part Two, the first part is largely talking head commentary on Jackson). The US Holocaust Museum has a library of recordings that are available to listen and watch online. These include audio recordings as well as films introduced as evidence. Stanford's digitization of the Taube Archive has transcripts of the trial as well as other legal documents.

Some of the above link are translated, but many are not. The IMT was a sprawling multi-lingual affair. The US did place considerable emphasis on translating the proceedings into print, but placed less importance on translating the audio and visual aspects of the tribunal.

The Robert H. Jackson centre has a youtube channel where they have the audio recordings of the entire IMT (you might have to scroll down a bit, the last parts were posted nine months ago). Unfortunately, only parts of the trial were recorded on video, so it's mostly audio. On top of that, the audio is all in the original language, so in order to be able to listen to the entire thing, you would need to be able to understand English, German, Russian, and French. Knowing English means you can listen to the US and British prosecutors present their cases, so at least you have that even if you don't have the other three languages. As for the NMTs, I've seen bits of video in various places, but as far as I know, they were not comprehensively filmed.

If you're interested in watching trials of Nazis in general, and not specifically the Nuremberg trials, I suggest watching the Eichmann trial here.