Important EU law cases from 1970 and 1977 in which the EU Court laid down that EU law should over-rule national constitutions. Since then, the principle that national laws must be amended to be in accordance with EU law, and not vice versa (the primacy of EU law) also covers national constitutions. Case 11/70 and 106/77.
Within the member states, the supremacy of EU law over national constitutions is only recognised in The Irish republic, Eire.
The future
As something completely new, the EU Constitution contains an explicit demand that the supremacy of EU law be respected. It also repeats the member states' duty of unconditional loyality, as well as a prohibition of conflicts between the EU and the member states being resolved anywhere other than at the EU Court.
Links
See also Costa/Enel and Karlsruhe.