[c] Global variables in header file

The currently-accepted answer to this question is wrong. C11 6.9.2/2:

If a translation unit contains one or more tentative definitions for an identifier, and the translation unit contains no external definition for that identifier, then the behavior is exactly as if the translation unit contains a file scope declaration of that identifier, with the composite type as of the end of the translation unit, with an initializer equal to 0.

So the original code in the question behaves as if file1.c and file2.c each contained the line int i = 0; at the end, which causes undefined behaviour due to multiple external definitions (6.9/5).

Since this is a Semantic rule and not a Constraint, no diagnostic is required.

Here are two more questions about the same code with correct answers: