I strongly believe the Constitution is still relevant and applicable to the world of today. The principles that undergird it continue to be valuable and in need of safeguarding. Freedom of speech and freedom of religion are still lacking in too many parts of the world for it to be safe to relinquish a document that enshrines these as inviolable rights. The Constitution also insists that arrests be open and charges stated publicly, which prevents people from being "disappeared" by secret police as has happened in other countries in recent times. It guarantees all citizen a fair trial, as well the chance to vote for the officials that will legislate government policy. It separates the powers into three branches of government with the idea that no one segment of the government or no one person should hold too much power. The above are simply a very few examples of the many sound and humane principles embodied in this document.
The major problem we have today is not the Constitution being outdated or irrelevant. It is still a sound, wise, applicable, and relevant document struggling under an environment in which it has been increasingly put under pressure. A strong case can be made that parts of the Constitution are being ignored: the founders, for example, might find the very long prison sentences and long periods of isolation people can suffer for non-violent crimes a violation of the Constitutional ban on "cruel and unusual" punishment. Further, the expansion of executive power and privilege would probably alarm the architects of this document.
It is also true that the Constitution needs to be amended from time to time to remain relevant and applicable to current needs. There is provision for that, and it has been done multiple times without violating its core principles. We might, for instance, now find it is time in the not too distant future to revisit how we elect Senators, given that the current distribution of population gives disproportionate power to underpopulated states. But these are issues that need to be decided by the people as a whole—and that is how the document is designed to be amended.
In my opinion, respect for the spirit of the Constitution and its attempt to prevent tyranny as well as to spread rights and democracy as fully as possible should be at the forefront of citizenship and civic duty.