I am trying to find out what the average duration of PhD studies are in the USA. Here in Spain it used to be 4 years, but it seems that Europe is moving towards a 3-year scheme since students are expected to do their MSc before they start. What is it like in the USA? Is some kind of shortening also occurring?
Each program is going to be different. Usually, the first couple years of a PhD program involves taking graduate level classes while the later years are dedicated to academic engagement in the discipline (for example, in Chemistry, you would do research in a lab.) If you have a Masters degree relevant to the PhD, you may cut off some or all of the classroom portion of the PhD program.
The qualifications for actually receiving the PhD also differ. You may need to get approval from an academic board (this is usually at least part of the process in any case), you may need to write a thesis, you may even be required to be published in an academic journal. (In the hard sciences, this is common.)
Because the requirements for getting the degree differ, the time may as well. For the most part, PhDs (with no Masters) should take between 4 - 6 years. Getting a Masters degree first may cut off about a year or so of that. While this is generally true, you will find many examples of people taking longer and I've known at least two people who graduated in less than 4 years with a PhD.
While this is an average, you'll want to get info specific to your desired University, the degree, and even the group (or academic adviser) that you choose to work for.
This varies so widely by discipline that asking for an average across all disciplines is unlikely to be very helpful. Most individual disciplines do keep careful records of this statistic, and it should be easy to search for them on (e.g.) google.
However, I would say with some confidence that no American PhD program requires or even expects its students to complete a PhD in less than four years. In some programs the "party line" is that it is desirable to complete the degree in four years, but in my experience this means that you start to feel the squeeze of increased teaching and/or decreased funding after four years, not that you get ejected from the program or forced to graduate.
I work in a discipline, mathematics, with a high entry cost but for which, once you acquire the necessary background and skills (with which a small minority of students do enter the program), there is no specific reason why you couldn't do all the work for a great thesis and write it up in a rather short amount of time, say on the order of a semester. Nevertheless I have met very few people who have completed a math PhD in fewer than four years. When we get to the upper echelons of talent, preparation and work ethic, this surely must mean that the culture of a PhD program strongly encourages students to stay for this amount of time.
To answer your final question: yes, many programs are trying to shorten their average time to degree as funding is being cut. In my own PhD program (mathematics at UGA) I was involved in an initiative to do just this: up until recently we guaranteed six years of funding to incoming PhD students without master's degrees and five for students with an incoming master's. We now guarantee five years to all students. Note that this does not mean that we do not have funded sixth year students: we certainly do. But it means that students will, throughout their time in the program, have to keep their eye on the five-year mark, which is something that our former arrangement was not doing: even very strong students would often stick around for six years for no especially good reason.
Finally let me also note that we changed (with my involvement) all our requirements to be independent of whether students arrive with master's degrees. We have found that the difference in the level of preparedness of such students is not significant enough to justify more stringent time-to-degree requirements.
The Survey of Earned Doctorates (http://www.norc.org/Research/Projects/Pages/survey-of-earned-doctorates-(sed).aspx) has detailed statistics. A summary report is http://www.nsf.gov/statistics/infbrief/nsf06312/ with breakdown by field, year etc.