Briefly about me: I’m enrolled in one of the top 10 programs and I took Ph.D. classes at another top 10 school when I was an undergraduate. In the last few years, I also visited several other schools and chatted with a lot of professors and students about this topic. I might repeat some of the things that have already been said by other people, but here are some of the things I learned.
In general, the ranking of a program matters enormously for several reasons. First, the best students are selected for and self-select into the most prestigious programs. To some extent it really is a self-fulfilling prophecy and no single individual can change that. Second, the top ranked programs offer the best opportunities for networking – they have a lot of prominent visitors from other universities that you can get in touch with. Third, how motivated and determined your peers are makes a big difference for how much you learn during your graduate studies and also how much you publish in later years, for example as coauthors. You will usually find a lot of highly motivated people at the top schools.
Note that although the top 10 programs probably offer a better training on average, individual professors can still be real disappointments and often programs outside of the top 10 also have great courses.
Fit matters, too, but here are some reasons why it usually doesn’t matter as much as ranking. Many people (if not most) change their research interests while they are going through the first few years of a Ph.D. program. You will learn completely new methodological tools and have a different perspective on political science research after your training. The type of questions you ask and you can possibly answer are likely to be very different from what you originally intended to do. The top 10 programs usually have a faculty that is diverse enough to make sure that you can follow your interests even if they change.
The ranking that I found to best represent the views of people in the discipline about the quality of different schools is the US News and World Report Ranking, maybe because it is based on the opinion of people in the discipline.
http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-humanities-schools/political-science-rankings
Another useful ranking is the placement ranking by Schmidt and Chingos that shows how successful individual universities are at placing job market candidates. The placement record is arguably the most important criterion for which program you might want to attend (it’s from 2007 though, so the information is a bit outdated and not 100% accurate in some cases).
http://www.people.fas.harvard.edu/~gillum/rankings_paper.pdf
Generally, always check the placement record of a school before you begin your studies there. It might not be your main concern at the beginning of your training but it will be later when you look for a job. If a program is not transparent about its placements that is not a good sign.
The top 3: Harvard, Stanford, Princeton
These three programs are outstanding for a number of reasons. They have some of the very best scholars in the field. When those people are on your dissertation committee, their connections will make it easier for you to get a job. The reputation of these universities will also ensure that their graduates get a good job outside of academia if their academic career doesn’t work out. Also, as I said above, the best students usually self-select into these programs, meaning that their superior position is constantly reinforced (it’s nearly impossible to break this cycle). From my perspective, there would only be two good reasons not to go to one of these if admitted – personal reasons (if, for example, someone definitely wants to live close to family and friends) or if you have absolutely clear and focused research interests for which there is a much better faculty match at another program - ideally still a top 10 program.
The top 10 (excluding top 3): Berkeley, Michigan, Columbia, Yale, UCLA, Duke, MIT, UCSD
If you’re admitted to two or more of the top 10, I think that each of them is worth a visit. The difference between these programs is not as significant as between the top 3 and everything else. All of these universities have their good and bad sides. I think it makes most sense to make a choice among top 10 programs based on which professors appear to be the best supervisors, which departments make the best impression on you, and in which city you can imagine to spend the next 5-7 years of your life. In general, the reputation of all of these schools is great and if you go to any of these programs what will matter most is how productive you are as a researcher (i.e. publications in peer reviewed journals).
The top 20 programs:
In most of the top 20 programs you will find professors with a great publication record and many also offer a good methods training. However, when it comes to job applications, the top 3 experience a very strong positive bias and the top 10 (without the top 3) experience a strong positive bias. This doesn’t mean it’s impossible to get a job if you’re coming from a top 20 program but it is definitely harder, given the same quality of research. You might want to consider this when making your decision.
Important: This is just my opinion, based on what I have learned about the “political science world” in the past few years. Please don’t treat anything I say as the absolute truth, also take the opinion of other people into account, and make your own informed decision when you decide where to spend the next few years of your life.