If you have a relatively stable, good job, but you don't feel that you are developing your skill-set or improving yourself in anyway, would you quit ?

Definitely yes....Adding skills is very important for career development. However, Quitting depends on the opportunities you are getting outside. By your preliminary research if you dont see the new organization giving immense opportunities to learn, do not change for only money.

I will say yes we should quit because we may have stable job, but unless we develop our skill and personality , we will not able to acquire higher position. And our career path will stop.

Only if I was offerred the job I find a good stable job that will provide my with the development I am lokking for.