The 14th Amendment, once passed, assured citizens that ALL the rights of the 1st amendment, 5th Amendment (self incrimination clause) 6th amendment guarantee the right to a speedy trial that is public and fair are imposed on the states. That's really heavy duty stuff. Many parts of the bill of rights are imposed on the states and they cannot challenge it unless they are willing to take it to the Supreme court.
A small note: In reading about this, my book on the constitution says that of all amendments the supreme court hears, this one is the one most often cited.