The philosophy of Law is a wonderful thing , it makes for interesting questions. I'm not going to give examples because on both sides you can find cases for and against the assertion of National rights over State rights. I'll use another angle.

By definition a nation is comprised of either separate states in joint agreement of nationhood or a group of separate individuals in agreement for nationhood. Your nation is called "United States of America", mine is the "Commonwealth of Australia" - both are comprised of individual states in joint agreement over unified sovereignty.

As part of that agreement certain rights and obligations are made by both parties. In general rights are kept by the states for the ease of government and transparency of the democratic process - we feel closer and more in tune with a more local government. In return, the state agrees to overall sovereignty being in the hands of a national government.

Without this underlying agreement, without the sovereignty clause, the state would not have the benefit of nationhood and thus would not be part of the nation at all, they would be a state.... I feel like I should use a QED statement here.

Its a case of compromise and overall, after countless tries at good government, the sharing of sovereignty by states within a nation works best, but for the national government to feel they ARE a nation, you must have a level of order and the supremacy clause ensures that order and thus nationhood.

..nationhood and sovereignty are very hard concepts to get into without going around in circles...

As in most things, the truth lies somewhere in the middle. The national constitution should protect the individual from the government's power, be it national, state, or local government. As such, the national constitution should trump state laws (as it also trumps federal laws).

However, the constitution should not be used to impose duties, limitations, and restrictions on the individual. There, local laws (state, mostly) should be what governs as what is acceptable behavior for society in one state may or may not be acceptable in another state. This is why proposals to use the US constitution to ban gay marriage for example are so ill-advised.

Overall, as a system of checks and balances, the constitution trumps all laws, but should only be used to limit government abuses and protect the individual from government tyranny. Federal laws should only trump state laws where there is a national interest (e.g. interstate commerce, national defense and security, etc.). State laws should limit individual behavior, but only where it impacts others significantly. Individuals in turn vote for federal, and state legislatures, assuring negative consequences to legislators who vote for bad laws or constitutional amendments.

A Constitution is the fundamental law of the land, it is crafted in order for a sovereign nation can define their system of government, powers , duties, procedures in which the people are to be governed. We cannot say that the constitution is trumping on state laws, we can only surmise that state laws should conform with the Constitution. When a state law does not follow with the Constitution, then it is null and void from the beginning. The remedy for the state governments is to amend the Constitution or to revised the new law in order for it to conform with the Constitution. That is how democracy works.

Governed states can always decide their own laws, as long as it is within the ambit of the Constitution. This is what we call supermacy clause. This clause is good for democracy, in the sense, that it is what is keeping the union between states together, without it, there would be chaos and anarchy in crafting the laws of the land.