Is there an inflation in the number of authors per paper?
I take inflation to mean that the number of co-authors grows faster than what the content/effort of the research merits: that would imply that if there is a non-negligible amount of such an inflation, it does affect the value of the authorship. 


Number of co-authors per paper is increasing
Co-authorship inflation is perceived as a problem
Perceived amount of contribution depends greatly on the position in the author list: first, last and corresponding author are perceived as contributing much, middle authors are perceived as contributing only a bit.  




Long version: 

First of all, the number of coauthors per paper is clearly increasing, e.g. pubmed provides statics about such questions:



Let me mainly take the optimistic position and list sensible valid reasons for increasing numbers of coauthors.

Some are well known and widely discussed


large combined scientific efforts like big instrumentation, the practical implementation of such long author lists widely and somewhat controversely discussed.
Increasingly interdisciplinary research
But I think that also the density of researchers has increased, which greatly facilitates collaboration.
E.g. I'm in a 100 000 inhabitant university town. The university has about 20 000 students and 7 000 employees (incl. professors - not sure whether this count includes technical personnel or only research staff). That alone is more than the whole town had inhabitants in 1900. PLus we also have a university of applied sciences and a number of non-university research institutes. I'm in of those reseach institutes, with about 300 employees.  So there are several thousand researchers with whom I can collaborate even person to person by bicycle/foot.
This high concentration of researchers facilitates intra- as well as interdisciplinary collaboration. These papers then naturally have more co-authors. Say, an "instrumentation" group develops a customized sensor for a group tackeling some application and yet other people develop the data analysis for the paper.    
In addition, email, skype and cheap travel (plus I'm in the luxirous position that there are basically no legal travel restrictions as I'm German and EU citizen) makes it much easier than, say, 30 years ago to know, meet and collaborate with colleagues from all over the world.
Specialization, particularly now that I'm at such a big institute.
E.g. where I'm now I usually receive readily prepared samples for measurements. Actually, being specialized on data analysis I often receive just the measured data (and I'm very lucky if people bother to have a chat beforehand on the design of experiments with me). Someone else prepares the samples and someone who mainly works on instrument development does the measurements. On contrast, where I was before everyone did all of that for their own topic and samples (of course also having emphasis on some part of this work flow). Of course all these people here contribute significantly to the paper.
But it also means that there is a continuous distribution size of contributions. I've somewhere seen a notion that weights the papers by 1/total no. of authors.


Of course, also abuse of co-authorship, such as honorary authorship, does happen, and maybe the specialization can become a salami-slicing of contributions.
I very much like the possibility of including a "contributions" section and decided to do that whenever possible. I think it can help checking against the abuse. At the moment (in my field), I think the existence of such a paragraph alone is a quite strong sign of no abuse of co-authorship.

But I think there are also valid reasons that mean that nowadays more authors are on a paper without the amount of work of the different persons involved having changed:


Nowadays, sometimes technicians who did a lot of the work (and often also contribute to the development of the lab methodology) are mentioned.
Also I believe that students who do research nowadays have a far better chance to end up on the author list. 
Maybe a gray zone, which also depends on customs/tradition is how to deal with the higher-up levels of supervision:


Vancouver says: providing funding alone is not sufficient (and of course the DFG goes along the same lines)
German tradition says: head of the institute is responsible for all that is going on in his/her institute, and thus is always included.
To be clear here: this does not mean (and AFAIK has never meant) only an organizational responsibility, but a scientific responibility, i.e. supervision of the project. The gray zone IMHO comes from the fact that the proper contribution can superficially look similar to improper (i.e. no proper contribution) -- it is difficult to judge from the outside: A very good supervisor may guide in a way that is hardly perceived. If this good supervisor is looking after a good student, after putting his intellectual facilities to the project may find that the good student does well, and not many changes are needed. This is a proper contribution. Yet it superficially can look very similar to a bad supervisor who does not contribute his intellect to the project or paper and just waves everything through - regardless of whether the input is good or not.  





I think this paper is interesting: 

Wren et al.: The write position. A survey of perceived contributions to papers based on byline position and number of authors,
EMBO Rep. 2007, 8(11), 988–991.
DOI:  10.1038/sj.embor.7401095
PMCID: PMC2247376


  In addition, we also asked respondents for their perception of general trends and attitudes towards authorship of scientific publications. Forty per cent of the respondents (35/87), for example, agreed that granting authorship to someone who does not meet journal authorship criteria was a common occurrence. Half of the respondents also agreed that author inflation makes it significantly harder to judge whether or not a candidate merits promotion.


While this does not answer the question whether there objectively is an inflation in co-authorship, it means that this is at the very least widely suspected and perceived as a problem.

Also, the outcome of that paper IMHO boils down to: perceived as authors are the first, last and corresponding authors, the middle authors are generally perceived far less. 

Personally, I share the suspicion that a significant amount of co-authorship abuse happens. However, my field is small and I think I have a reasonably good overview of what is going on. This includes a (subjective) idea of where I'd suspect honorary authorship or small contributions and on the other hand also some idea of who likely contributed what (specializations) to the paper. In addition, of course the listing of the instituions makes a lot of that clear (e.g. if someone from a statistics department, someone from a clinic and someone from a spectroscopy lab is listed that gives me a very good guess who 
did what).