Define monarchy. Does it mean a strictly hereditary system, or perhaps one in which the leader is chosen from within a narrowly defined group. For example, the Brits has a strictly hereditary system meaning, other systems are more flexible (e.g. the Saudi monarchy, the Catholic Church, and the way the frum community chooses its leaders with gedolim emerging from a narrow somewhat hereditary class of persons).
The opposite of a monarchy is a republic. Republics, and Monarchies, can be based on democratic or non-democratic principles. Many Republics are dictatorships, and many monarchies are friendly and democratic.
From a Torah perspective what matters is what they do. We have had friends (and enemies) who were presidents, and others who were kings. Similarly we have had democratic friends (and enemies), as well as un-democratic ones.