its my understanding that due to the supremacy clause, federal (constitutional) law trumps state laws. in some cases, state laws can grant addiitional rights, but they can't abridge the rights granted by the constitution.
One by one, the amendments have been/are being slowly incorporated to protect individual rights against State governments as well, as the result of Supreme Court rulings: http://en.wikipedia.org/wiki/Incorporation_of_the_Bill_of_Ri...
To date, the first, second, fourth, partially fifth, (by and large) sixth, and partially eight amendments have been incorporated, i.e. apply equally to both State and Federal governments. The 2nd (the right to bear arms) was the most recent one, incorporated in 2010 here in Chicago.