File System Corruption
A drive that's recognized and mounts, but throws errors, freezes when opening certain folders, or shows files that vanish and reappear between reboots, isn't dying — its internal bookkeeping has gotten inconsistent, and that's a considerably more forgiving problem than physical damage usually is.
What's actually happening
File systems maintain a set of interlinked metadata: directory entries, allocation tables or bitmaps, and often a journal log of recent changes. Sudden power loss in the middle of a metadata update, read errors from a drive that's quietly starting to fail, or a software bug can leave these structures internally inconsistent — a file marked as occupying space that's also marked free, for instance, or a directory entry pointing to a location that no longer holds what it claims to.
How recoverable this really is
The odds here are usually good, since inconsistency isn't the same thing as loss — the data is generally still there, just described incorrectly by the file system's own records. Where this goes wrong is almost always in how the inconsistency gets fixed, not in the original damage.
The general approach
Proper recovery here works by reconstructing a consistent picture of what's actually on the disk, cross-referencing the file system's structures directly rather than trusting whatever the built-in error checker reports. Critically, this is done against a byte-for-byte image of the drive, not the live drive itself, so nothing about the process can make the original any worse.
Built-in repair tools — chkdsk /f, fsck, Disk Utility's First Aid — are designed to make a file system internally consistent again as fast as possible, not to preserve every recoverable file along the way. Run against a drive that actually holds data you care about, they can permanently delete files that a careful recovery process would have gotten back intact. Image the drive first, and repair — or better, recover — second.
Practical, step-by-step guides for specific recovery software will be added here as separate linked articles.
This page describes the general situation, not a guaranteed fix for your specific case. If you'd rather have someone experienced take a look before you try anything, see what a hands-on evaluation looks like.