Getting file hashes can be quite useful. This can be used for instance to make sure that backed up files are not corrupt or modified (by generating hashes before and after the process), or to make sure that no one tampered with an important file.
You may see it on download sites as well, but the use there is limited. The reason is simple: if an attacker managed to change the download file, there is a chance that the website was compromised as well. This could theoretically at least mean that the file hash displayed on the site was modified