I've been admitted to multiple PhD programs, how should I choose between them?
Advisor

Your advisor will be a really, really, really key part of your PhD experience, and can make all the difference between success and failure. 

There are many different advising styles, and you should learn more about potential advisors to find one whose style works for you.  

walkmanyi sums it up:


  Many don't speak about this too often, but with an advisor you are not only choosing a field of interest, but you are choosing a mentor. By all means, you want to "tick well" with him/her. There is not much good for a PhD student having a star researcher advisor whom they see once in a quarter and who is a sociopath on a personal level (this is a bit too extreme, but think about it as a continuum between extremes). Choose somebody with whom you will be able to work, whose example it is worth to follow, from whom you want to learn, not only the scientific stuff, but also workstyle, level of quality he/she strives for, etc. These soft reasons are often more important than anything else.


Fomite has a fairly comprehensive answer on how to judge potential advisors by looking beyond their recent publications:


  There are a few things I would generally look at in a potential advisor beyond just their research/publications:
  
  
  Who were the co-authors on their papers? Are they actively collaborating with people in your field - people who could be potentially useful for post-doc posts, etc.? Do their students often show up as primary authors on publications, or are they invariably buried in the middle of a long list of authors?
  Personality. This goes beyond just do you like the person. Do they prefer frequent updates, meetings and the like, or is the occasional check-in enough? Are they a morning person and you prefer working nights, or the other way around? If you send a long email, would it get answered, or do they not often fail to answer emails? I've had some professors who I'm very fond of nevertheless would make poor advisors because of wildly disparate working styles.
  How are their students funded? Your funding stream can have serious impact on your completion time and productivity. If every semester, its a desperate Pick-N-Mix of funded side projects, TAships, etc. you're going to have a lot on your plate that, while potentially an interesting experience, will slow down your progress.
  Where do their students end up? Do they have decent career trajectories? Are they supportive of alternative paths like industry or government?
  Rank and age. A young professor might be more aggressive and eager, on the other hand they're less established, don't necessarily have the same level of institutional support, and if they're not yet tenured, its possible they'll disappear. An older professor may be more established and stable, but might not use "cutting edge" techniques, or feel less of an internal drive to publish.
  


Henry adds that there may also be some benefits to having an advisor who is generally well-liked by his/her peers:


  I'd add to your list how your advisor is viewed in the rest of the field. Not just on the quality of research (though that's important too), but again, how much people like your advisor personally. Again, a small factor, but having other people in your field like your advisor can make a difference.


But really, the best way to find out about a potential advisor is to talk to their current students, and we have plenty of questions for you to ask!

Piotr Migdal says the most important question to ask is 


  Are you happy with your PhD in general?
  
  It covers a lot of issues, but usually you don't want to do a PhD in a place where students are unhappy and frustrated. The good thing is that if students feel really bad, they rarely hide it.


but he adds a few more, too:


  
  General contacts on the line student-advisor (How much contact and support can you expect, both for research and administrative stuff?).
  Funding (Is it a problem or a non-issue, e.g. for attending a conference?).
  Research (What the actual research looks like? What is the toughest part, biggest emphasis on, the most time-consuming part, etc?)
  How much time does it typically take to finish PhD? Does it happen often that someone drops out?  
  


Suresh suggests asking:


  
  does PA [potential advisor] have time to meet with you when you need help ? Or does PA [potential advisor] want too many meetings ?
  how much guidance are you given ? Too much ? Too little ? 
  is the relationship "work only" ? Do you talk about non technical academic issues ? 
  


Theresa Liao has some more good questions to ask current students:


  
  Do/Did you (the current/former PhD) enjoy working in this supervisor's research group?  Do research group members work with each other collaboratively and help each other? And ask the PhD student to elaborate. 
  
  This question tries to get at what the research group dynamic is. This is fairly important in my opinion - the last thing you want to concern yourself with is politics in the research group. I have seen PhD friends frustrated by this.
  
  
  Ideally you should ask this question in a less formal setting (some grad school visits will have time for social events). And sometimes you meet grad students who are comfortable sharing their experience openly. If you are not comfortable asking this question, as it can be an awkward question for the supervisor's current PhD, you can simply observe the interaction between group members, and between group members and the supervisor. 
  
  
  Is the supervisor generally available? Does it take a long time to arrange a meeting to meet with the supervisor (used to be the case with my supervisor because he was so busy)? Does the supervisor respond immediately and effectively (another friend's supervisor tend to leave questions to last minute)?
  Are group members expected to work 24/7 or 9-to-5? Some supervisors expect you to reply to emails immediately, and some work strictly business hours. 
  Does the supervisor take a hands-on or hands-off approach? Are students expected to be really independent with lots of freedom, or are they guided/directed along the way with less freedom?
  Does the supervisor support his/her students to consider career paths outside of academia? Some supervisors only want their students to go into academia, and it will be harder to discuss options with such supervisors.
  
  
  For Q2-Q5, the right answer will depend on your own preference - what you want is a supervisor whom you will work well with.