To expand on Henry's answer: "The powers that be" is a set phrase quoted from Romans 13:1.
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God.
In that context, it means "the temporal powers that indisputably do exist in the world," so we can rule out explanations that call on the subjunctive mood — here Paul isn't talking about "the powers that [may or may not] be", he's definitely talking about what we today would call "the powers that are."
So, why do archaic English sources use the form be where modern English would use are? Well, here are many partial answers all together in one place: Abbott's A Shakespearian Grammar quotes Richard III, act IV, scene 4:
Where is thy husband now? Where be thy brothers? Where are thy children?
Abbott suggests that Shakespeare (and also the King James translators, who were working in English at the same time as Shakespeare) preferred be to are for the plural indicative form basically because it sounded better on a case-by-case basis; with maybe an additional connotation of uncertainty.
So, as a rule, it will be found that be is used with some notion of doubt, question, thought, &c.; for instance (a) in questions, and (b) after verbs of thinking. [...]
Be is much more common with the plural than the singular. [...]
Be is also used to refer to a number of persons, considered not individually, but as a kind or class. [...]
But it cannot be denied that the desire of euphony or variety seems sometimes the only reason for the use of be [as opposed to] are.
— Abbott, A Shakespearian Grammar, "Auxiliary Verbs", sections 298–300.
Let's face it: "the powers that be" sounds much cooler than "the powers that are", and the guys who wrote the King James Version knew that just as well as you or I. :)