This question might be too conceptual.
Congruences between modular forms (due to Shimura, Hida, etc) are really amazing. I know that the eigencurve construction are closely related to these relations. The basic reference is "The Eigencurve" by Coleman and Mazur. Besides, I think "A brief introduction to the work of Haruzo Hida" by Mazur is a good introduction.
It seems that we at first prove the congruence and then interpolate them into a family, like the Eisenstein family, and the property of the eigencurve are deduced from properties of modular forms.
So I wonder conversely, can the eigencurve construction explain (prove) more congruences between modular forms (not just these used in building the eigencurve)? Or other interesting facts about modular forms? For example, see section 5 of "A brief introduction to the work of Haruzo Hida".
I type slowly, sorry...