Monarchy/Body of Unelected Rulers, eg. Theocracy, Oligarchy, et cetera: You end up with bribery and patronage unless you severely cut the power of the King or Queen. Which no longer makes it a monarchy...
Anarchy: Nothing would ever get done, nothing would be created, no work would be done. Much of public works - schools, hospitals, safety measures - are controlled by law. No law = no control over the less sane members of society. Which, despite much verbiage to the contrary provided by the text-speak theses provided by teenagers who dye their hair red and think Linkin Park have actually made a listenable album at some point in their overly long careers, is not gonna be a good thing. Try having decent medical practice when bricks keep hurtling through the window.
Communism: In theory it's sound - so long as everyone joins in. Otherwise it simply won't work, even Marx and Lenin realised this. Marx even put it in Das Kapital! So yeah, that's communism out.
We are thus only left with Democracy. It may not be perfect, but it's the not only the best form of government we have, it is the ONLY feasible form of government we can come up with.