Where and what you find of usage statistics (downloads, uses, reads or accesses) may depend on publication type and platform on which it is hosted.

Articles:

For articles, citations would in most cases be a preferred statistic as they are generally considered the mark of reuse. However, usage statistics can provide additional information (especially for recent articles). For recent works, consider using together with mentions in news and social media, which are another short-term measure.
Some journals show reads/downloads/accesses on the webpage of the article
Web of Science has a statistic called "Usage count" for articles in the database, but this only shows interactions via the Web of Science platform and thus is likely to be an underestimate of true usage.

Books and chapters:

For ebooks, see if your publisher provides statistics for reads, downloads or sales. You may be able to see this on the page of the book itself. For physical books, sales numbers may be available.
Use Worldcat to find how many libraries/library consortia worldwide hold a copy of your book. Enter a location under "Find a copy in the library". For example, this book is held by about 300.
For textbooks, you may be able to find statistics that illustrate educational use (e.g. number of courses, number of institutions etc.)

Datasets:

Software and packages:

Some code archives provide downloads and views (e.g. Zenodo)
Stars, forks and watchers from Github have also been suggested as a measure of software impact (Dozmorov 2018)
For R packages in CRAN, some methods for gathering download statistics are listed on Stack overflow - Check how many downloads a CRAN package has

Preprints:

Some preprint servers will provide statistics for views, full text views, and pdf downloads (e.g. bioRXiv)