This post will talk about the current state of standardized open file formats
Video Files
Mostly standardized. Video files can be played pretty much everywhere, however there are still legal issues with some patent encumbered codecs, subject to licensing fees. Some codecs such as VP9 are free and open, however.
Intermediate codecs used for video editing rely on fully reverse engineered closed intermediate codecs such as Apple ProRes. This can be problematic from a legal point of view in some cases.
Audio Files
Standardized. Audio files can be played everywhere, patents for mp3 expired, and there are other free alternatives for lossy audio coding such as opus.
Office Work
This is where things get really ugly, in my opinion.
PDF Files
On paper, PDF is supposed to be an open format with public specs. In practice, few PDF readers besides Adobe Reader managed to implement everything.
This is a big problem for PDFs that contain multimedia functionality such as videos or animations. Videos and animations embedded in PDFs cannot be read by Chrome, Firefox and most FOSS PDF viewers. The only PDF reader who reads them reliably is Adobe Reader.
For electronically signing PDFs it's a similar story, not many PDF readers can do it reliably, besides Adobe Reader.
In the past, proprietary content used to be embed in PDFs such as Flash. When Flash was discontinued many of these PDFs cannot be read.
Editing PDFs semi-comfortably pretty much require paid Adobe Acrobat, and even then it is still a pain. PDFs are not a proper editable format.
Non-editable static text and images, and some fillable forms should work on Chrome, Firefox and most other FOSS PDF viewers.
I don't consider it a great standardized format, if we pretty much need Adobe Acrobat to get its full functionality and be able to read every PDF. I don't think that it is a coincidence, especially when you consider that PDF used to be a completely closed format guarded by Adobe.
Word Processor/Slideshow/Spreadsheet files
Terrible, it's a complete mess. The most popular format is Microsoft's OOXML format. The specifications for it are a long ~3000 page long document with a lot of bugs, exceptions, and even undocumented behavior. I will skip you the story short: only Microsoft Office can reliably open these files with full functionality without butchering the formatting.
All other Office suites entirely rely on reverse-engineering a moving target.
If you want to read more about this topic, I invite you to read this.
The Open Document Format is a promising alternative, but it has many problems. First of all, there is nothing to prevent Microsoft Office from butchering Open Document files and not properly implementing the spec. It would mean that editing, saving and opening Open Document files would be de-facto not supported in Microsoft Office. If they do it this way, there wouldn't be any public backlash or legal sanctions due to plausible deniability.
Secondly, some people complain about missing functionality in the Open Document spec. This was one of Microsoft's justifications to adopt their pseudo-standard instead of the Open Document format. This issue is impossible to solve, as no file format is perfect. People should spend their energy improving an open document format instead of migrating to proprietary formats each time something is missing.
Thirdly, no properly compliant Open Document format editor and viewer is preinstalled on computers by default. This is a big one. Browsers cannot view nor edit Open Document files, and no Open Document editor is preinstalled on Windows or Mac. If people install an Office suite, it is probably going to be Microsoft Office, which has a vested interest to not play nice with Open Document files.
If we want to collaborate or share with others local editable document formats, we are out of luck, there is no practical and satisfying solution. No open document format is widely adopted, many people are locked into using proprietary file formats.
Workaround
The most popular current workaround to avoid this interoperability problem seems to use cloud services, like Google Docs, but it's not ideal for privacy, they can be discontinued, they don't make it obvious or easy to work with third party word processors if it is even possible, and they don't make it easy or obvious to work offline.
Conclusion
I could go on and on with other proprietary file formats like some ebooks, mangas, .psd files and so on, but I think that it will be enough.
We have made some progress compared to the 90s, but it's still quite bad and we have lost some competition in the meantime (Microsoft Office is close to a monopoly on local office suites).