A constitution is necessary, I would say, for every nation. A constitution is like a recipe for a successful nation. Not having one is a recipe for disaster. A constitution is meant to establish the rights of everyone, lay out the duties of and limits on government, establish procedures for an orderly change of government, and provide the wherewithal for the enforcement of the constitution and the laws of the nation.
Without a constitution, people's rights are by no means guaranteed. The constitution is a promise to the people that the government will respect the rights enumerated. Some examples are freedom of religion, freedom of speech, an entitlement to education, and an entitlement to health care. The United States is just one constitution among many, and they do differ in some ways. (I have included a link for a discussion of the English constitution, for comparison.) A constitution can really be viewed as a kind of contract. Without this promise or contract, leaders may do as they please to people, arbitrarily and capriciously, and they do.
A constitution creates the arrangement of the government, what branches of government there will be, what powers and limits each branch has, what duties each must carry out. For example, the United States Constitution sets up a three-branch system, and each section has enumerated duties and limits of various kinds on its power. The president may not make laws. That is up to Congress to do. But Congress cannot run the military. That is the president's duty and power. Without this recipe, it would not be clear who was supposed to do what, and government would be a ceaseless power struggle, with nothing getting done.
The constitution provides for a change in power without war, revolution, or military coups, which is how some countries come to changes in administration. There is a provision for term limits and elections of new government officials. This orderly transition is almost impossible to achieve without a constitution to govern it.
A constitution provides within itself the means to ensure its own enforcement. For example, the Fourteenth Amendment of the United States Constitution specifically states that Congress has the power to enforce the amendment. On a more general level, the Supreme Court of the United States has the power to interpret the Constitution, and while it does not have an army, as some people are overly fond of pointing out, the executive branch does have federal marshals, and part of their job is to enforce Supreme Court interpretations of the Constitution, as they did, finally, after schools were integrated after Brown v. Board of Education (1954). Without a means of enforcement of its terms, though, a constitution is an empty promise.
All things considered, I would much rather live in a nation that has a constitution than I would in one that does not. Even a democracy is meaningless without one.