On a personal level, I learned an incredible amount going through the Nanodegrees, especially because of the project-based instruction. I've taken 20+ courses at edX, Coursera, and Udacity and went through pretty much all the curricula at Code School and Team Treehouse. I can safely say that Udacity Nanodegree was the most positive, valuable experience out of all of them--you're not just taught what to do, you're taught how to think.
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Here's a copypasta response I wrote on Quora to the question, "How valuable is a Udacity Nanodegree certificate?"
The Nanodegree program is still new, and chances are, a potential employer won't be familiar with it, nor even heard of it. If they have, they'll probably still evaluate you based off of your resume and portfolio.
A Nanodegree certificate won't guarantee you employment, clout, or value on its own merit... at least not yet. But by going through a full Nanodegree program, you will finish with a full, robust portfolio to demonstrate to an employer and say, "Here are all the projects I worked on. These are the skills I learned while doing them. This is the quality of work you can expect from me."
Like any educational program or institution, you can skate by with the bare minimum and earn a piece of paper. If you do that with Udacity, I think you're missing the point, and your potential employer will see nothing but your bare minimum.
I'm a graduate of three Nanodegrees, and as such, evaluate it much differently than most other people. I have never placed much value in certificates or diplomas, and I always evaluate applicants based off of their portfolios and the knowledge and potential they bring into an interview. That said, I can safely say that if a resume with a Udacity Nanodegree arrives in my inbox, I will know that at the very least, that applicant has the will, drive, and discipline that's needed to complete a self-paced, rigorous course-load.
"Show me your portfolio," I'll say.