It started as my old Activity report where I was not completely successfully trying to persuade administration that Research is not synonymous to Publication in peer-reviewed journals. Not that administration did not agree with my arguments but referred to Standard practice which IMHO is no more sustainable. I updated my arguments few times for this Apology.
Currently peer reviewed is an almost synonym to printed or paper. I believe that for the majority of paper journals their time is running out and they are on the artificial life support (since younger colleagues are in the dire need for peer reviewed publications). Time is for electronic publications in pdf format (I am talking about Math and Friends, for Social Sciences other formats could be preferable but even in that case I bet on pdf) which
While it is true that most of the printed journals are also distributed electronically, they are not truly digital as articles published there are not optimized for digital media and have almost none of the properties listed above. They are just electronic copies of the paper articles. In contrast many if not majority of articles in arXiv are much closer to ideal digital papers.
Very recently Millennium Prize Committee recognized publications in arXiv as meeting requirements awarding G. Perelman for papers which were published there. Also in contrary to popular belief arXiv accepts large monographs (just procedure is different: private communication from one of the editors).
How peer reviewing is important? In articles I reviewed last few years I found once a critical error (small paper by noname author), in other I found no visible errors but some I found not of the great interest. The trouble is that when article by the author(s) who are really serious mathematician looks good and correct, it often refers to 3 previous papers by the same authors and verify correctness one needs to read 200-300 pages of dense material, often containing "modifying arguments of the proof of Lemma 3.5  one can easily prove ..." and in most of the cases it is impossible within reasonable time. Basically peer-reviewing became a filter against obviously erroneous and/or mediocre articles but it randomly slows down publication of the good ones.
Further, printed journal have fixed volume and the quality of publication just fluctuates following the size of portfolio.
My book of 1998 was ~800 pp of printed in small fonts (Springer wanted to save at the expense of the eyes of the readers), the new one I expect to be at least twice (2.5 more likely) as large and it will include a host of the new material, and a lot of the previously contained material expanded and a lot of the really old material which was not included in the 1998 book, rewritten; in particular I am going to use many of the features listed above, including extensive graphics.
So, my large articles, published during last few years (on my website and in arXiv), are actually chapters of this book. It is not precisely true because they are self-contained in the certain degree but to publish article in the journals I would need to make them much more self-contained (as a journal reviewer I never let pass articles with such external dependencies and I do not expect others). Further, these articles would be published in the different journals, pass through different referees which would mean different requirements and would result in the loss of the uniformity, including uniformity in notations and appearance. This is exactly opposite to what should be done to make a book out of them. I consider such preparation in two different ways (for the journal and for the Research Monograph) a waste of time which I cannot afford.
The other problem with the printed journals is the skyrocketing cost of them and simultaneously decreasing library funding. The number of journals is growing as well. Together these factors decrease circulation of these journals and articles in them. Electronic subscriptions are also becoming more expensive. Some people blame this to the greed of publishers, some on growing printing costs, and some insiders claim that the most expensive is a preparation (i.e. typesetting). The latter is very troublesome as the main task of the typesetters (who more often than not are very qualified TeXnicians or even TeXperts) is to provide uniformity of the articles and their compliance with the journal standard. This is very nice but keeping in mind that usually the reader reads just one article in the given issue of the journal but few articles of the same author published in the different journals, the uniform appearance of the articles in the journal matters much less than consistency inside of the sequence of the articles of the same author.
Furthermore, some decent mathematicians work in the institutions with libraries having no expensive mathematical journals. F.e. when I lived in USSR I was getting mathematical articles printed in non-USSR journals only either as preprints sent by the authors or as articles to review for Mathematical Reviews, Zentralblatt fur Mathematik or their Russian equivalent РЖ Математика, plus trips to Moscow or St. Petersburg libraries. I don't believe that situation changed drastically and I believe that, say, in Russia mathematicians from all the cities except Moscow and St. Petersburg have very limited if any access even to the most prominent foreign journals.
Many journals have the single purpose: to provide publication in the peer-reviewed journal rather than provide a circulation. However as these journals are not of the world repute there is a fight to be published in one of the most prestigious journals, especially in Annals. Proving how great you are became as least as important as proving theorems.
Actually, many mathematical articles are also the chapters of some books, which has been neither published, nor written, nor even planned. There are plenty serial articles which are heavily referring to the previous of the same authors, so to read such article one needs either to go to the library or to use an electronic version of such paper. However when the previous paper was written the author usually was not thinking very clearly about the future one and the results were formulated not in the best way from this point of view. So, the next articles contain explanations that the results of the previous ones could be easily modified in a certain way and eventually one gets a series of patches over patches which creates a complete mess. In contrast, e-artcles could be easily modified and corrected, and if crucial changes are made, there could be few dated versions of such article (CVS or SVN approach).
In April 2007 I wrote "I think that in a half year I will finish to research what I have been planning and to finish this book in 2009 just to publish it in 2011 or 2012 (which would be 100 years from Hermann Weyl's articles which started this field). However one could never know: sometimes what is planned as a small and a fast research turns out to be long and laborious, opening new horizons and going to them requires years (it happened with me many times)."
And in fact, in mid-December 2007 I started my book. As expected this book will contain new results which make the whole building more complete. Some of them are important new results appearing among old ones. However in September-December 2009 I was writing Chapter 15 completely devoted to major new results. At this moment I am planning to finish it in 2015.
The writing of the book has an inner logic: often theory constructed in the series of articles is not logically complete despite everything is rigorously proven. This incompleteness is not always easily observed and sometimes missing elements are not large enough to justify a new article. But writing a book one can fill these logical gaps and the whole theory looks much more polished.
Another things: some (and by no means minor) improvements could be inserted after the corresponding part is written because working on one of the next parts can trigger certain ideas. So working on the book is non-linear process while working on the series of published articles is a linear in the large scale (and non-linear in the small scale). When author has submitted an article and later finds a significant improvement, he/she faces a dilemma: either to submit a major modification to the article and thus delay its publication or to write another article and I suspect that the most take the second road (as I did when I was younger).