happened to - happened with

Like in "What has happened to you?" vs "What has happened with you?"

What's the difference?
I take it the former form (happened to) is more common, but is there any semantic difference?

Yes there's plenty of semantic difference. No.1 is passive and No.2 is active.

Oh, we've got celebrated writers here.

Dear SHifter, "happen with" is in many cases a mistake, a calque from other languages.
Sure Google gives a great number of hits, but some are not relevant, for instance
<This had not happened with the same degree of effectiveness >.
I guess "happen with" means *with somebody present there*.
Ayn Rand might have condescended to an explanation rather than just a brief statement.

<No.1 is passive >

Rubbish. There is no passive of "happen". If there was, it would be "It has been happened", "it was happened", it is happened".

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Happened to = physical event, body level.

Happened with = psychical event, mental level.