Holy cow, I wrote a book!
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Why are INI files deprecated in favor of the registry? There were many problems with INI files.
The registry tried to address these concerns. You might argue whether these were valid concerns to begin with, but the Windows NT folks sure thought they were.
Commenter TC notes that the pendulum has swung back to text configuration files, but this time, they're XML. This reopens many of the problems that INI files had, but you have the major advantage that nobody writes to XML configuration files; they only read from them. XML configuration files are not used to store user settings; they just contain information about the program itself. Let's look at those issues again.
XML manages to sidestep many of the problems that INI files have, but only if you promise only to read from them (and only if everybody agrees to use a standard-conforming parser), and if you don't require security granularity beyond the file level. Once you write to them, then a lot of the INI file problems return.