There are many good points raised in niemiro's answer, but I wanted to emphasise a couple things.
- Puzzles should be self-contained - this avoids any of the considerations raised regarding the possibility that data goes missing if its hosting location goes off-line. We strongly recommend that, if it is possible for all the information to be provided within the posting of the puzzle itself, that it be put there. In particular, for the puzzle referenced in the question here, the data in question didn't have to be encoded the way it was; rather than requiring someone to know that "lzma" and "pickle" are meaningful to enable them to recover data from an encoded binary file, the data could have been provided in a different way (perhaps even not encoded at all) that would have allowed it to be more readily presented and used in text form within the puzzle posting proper.
- Images (per se) are fine; they already have a home at i.stack.imgur, and the SE interface provides integration to streamline use of that hosting site. They are displayed directly in the browser and, even when used to steganographically embed data, extracting RGB- or bitwise-encoded information can be done with online or local tools without particular risk.
- Other data is more troublesome. We never want users to download data of unknown provenance to their own computers, as that's a Really Bad Idea™.
- If there is data required to solve the puzzle, but which is difficult or impossible to present in the puzzle body or in an image file, it is very likely that this puzzle is not going to be appropriate here, as required data is not self-contained in the posting or its images.
- If there is optional data which can provide solvers useful templates, data visualization, or the like, this data can be provided but should be given in a way that does not require downloading binary files make use of it. For example ...
|Type of data
||How to host
||pastebin can display bulk text in user's browser, and can be cut&pasted safely to local machine if desired
||read-only Google Docs spreadsheet
||online runtime environments, like tio.org, allow code to be run and even modified, and output viewed, without downloading code or installing an interpreter
||Online viewers, e.g. http://www.viewstl.com
These allow data to be viewed/manipulated in a browser without downloading it, and generally allow the text of the data to be cut & pasted locally if desired, all without having to download a binary file. The sites specifically named here are considered reputable and don't require users to sign up to view content hosted there.
Keep in mind these should really only be used for optional data; there is no guarantee that any of these off-site resources will remain available, and we don't want a puzzle to be lost because vital data disappeared.
- Executables are never okay.
- Archive file formats are not okay. That means
.zip .tar .tgz .7z .rar and the like. These not only are binary formats themselves, they can contain other binary files as well, and as they contain entire (named) files there is a potential for existing files to be overwritten, for harmful files to be included amongst innocuous ones, and/or for files to be saved in unexpected and unwanted locations that end up causing harm later.
- Encoding executables or archive files in other ways (encoded as text, smuggled in image steganography, etc.) is still not okay (and attempting to hide potentially harmful content this way is a great technique for getting unwanted attention from a moderator!)