Can a PhD be crowdfunded?
While I'm sure its possible I haven't been able to find any examples of funding an entire PhD. However, there are quite a few examples of people crowd funding smaller individual research projects. I think there are two main reasons for this cost and accessibility.  

Cost

It is really quite expensive to fund an entire PhD. If we look at the costs of a PhD (in the UK) we get.


University fees: ~£4000 per year (~£15000 for non-EU students)
Living expenses/stipend: ~£12000 per year
Conferences/equipment/other stuff: ~£2-3000 per year +
approx £20000 per year for 3-4 years = ~£60000 (>$100,000)


Compare this to the average successful crowdfunding amount of $7000 and you'll see why it'll be hard to raise that sort of money and would require a very strong marketing campaign. Which brings us nicely onto

Accessibility

One of the things a successful crowd funding project needs is a good sales pitch. You need to have a very clear goal that will excite lots of people to fund you. Not many PhD projects I know could possibly fall into this category. 

For conventional crowd funding you also need to give something back to supporters to make it worth their while. While I suspect this would be less true for crowd funded research there are many people who might like to support you but cannot/will not without the prospect of some tangible return.

What seems to be more common is to fund smaller individual projects for ~$10-20000. For example http://blog.gogetfunding.com/crowdfunding-statistics-and-trends-infographic/ although there are some bigger and smaller examples in this article http://www.onlinephdprograms.com/dollars-for-doctors-a-guide-to-crowdfunding-academic-research/