How many arXiv papers are uploaded in their final (refereed) versions?
It is a lot of work to find out which paper in arXiv has actually the same content as a published paper. However, taking arXiv's journal-ref field as a surrogate indicating which paper has a journal version out, I arrive at these fraction of papers: 


So it looks as if the gut feeling that this is field-dependent is true: high energy and nuclear physics have consistently high fractions of papers with journal-ref field set. On the other hand, this seems far less common for maths papers.  Note that a certain drop at the end is to be expected as the preprints may be uploaded to arXiv considerably before the paper is accepted, printed and the journal-ref is updated in arXiv. 

Here's the marginal plot over all fields:
 
So overall, about 45% of the papers have a journal-ref. However, it is set for almost 60% of the 2001 - 2007 papers. Whether this is a real decline or just the lag between preprint and paper publishing remains to be seen (in a few years).

Also, neither the overall nor the subject-dependent trends seem to have a convincing increasing trend, even if the decline due to "not yet published and updated" is assumed to be the sole cause of the decreases. 

For the complete picture, here's the development of total number of papers:


and number of papers with journal-ref set: