The original question was, "Do we need government?"
That question is insufficient if answered "yes" or "no." The existence of government is not a choice like whether or not we should have eggs for breakfast. It is a reality of human existence, and it is tied to the fact that mankind has willpower. This willpower effectively makes each person his own government. He is manager of his own affairs, and he can interact, cooperate, oppose, or trade with others. In other words, he is a sovereign individual.
When anarchists talk about their namesake, they (or admittedly some of them) do not mean to remove government altogether. That would mean taking from mankind one of the fundamental things that make him human. On the contrary, anarchy is simply removing the coercive rule of one over another. In this scenario, men still interact, but they do so freely in a relationship were neither imposes his will on the other. The alternative scenario involves one becoming the master, and one becoming the slave to the master's will (even if ever so slightly).
Of course, one could say that if one man, of his own free accord, gave up a portion of his own will to be governed by another, no one could argue that rule. This is true, and this is also the way that many kingdoms, republics, and dictatorships began. An honest anarchist will not deny the valid creation of such institutions while questioning whether the non-coercive foundation of those governments has given way to the same, continuous power play that has plagued the peaceful, the simple, and the just.