I'm not a subject matter expert here, and just going based on my memory and what some friends have said, but according to http://en.wikipedia.org/wiki/Approximation_algorithm,

NP-hard problems vary greatly in their approximability; some, such as the bin packing problem, can be approximated within any factor greater than 1 (such a family of approximation algorithms is often called a polynomial time approximation scheme or PTAS). Others are impossible to approximate within any constant, or even polynomial factor unless P = NP, such as the maximum clique problem.