Question: I'm redesigning my business cards, and since my last design, I've spearheaded a few projects for some high profile clients (in their respective regions).
Is it a good idea to add their logo to the back of my card titled 'clients?'

Answer: 
Unless you have specifically asked for permission, you should not for two reasons:

1. Having their logo on your business card says nothing about the works you did and provides limited value to new clients. It may give the false impression that they are endorsing your skills and work
2. Most companies have trademarked or copyrighted their logos, so without their permission you are not allowed to use the logos. Any company large enough to be worth having on your card probably does not want random people advertising the relationship.
Absolutely not. If need be you could hand write contacts on the back of the card. 

In general the notion is that you could supply references on request. You'd have to be able to supply a real contact in whatever company, not just the company name. Depending of what you did and what job you are applying for you might need to annotate your reference list for the particular situation.