Is this statement of conservation of charge circular? According to Wikipedia:

A closed system is a physical system that does not allow certain types of transfers (such as transfer of mass and energy transfer) in or out of the system. 

According to my textbook, the principle of conservation of charge is:

The algebraic sum of all the electric charges in any closed system is constant.

Isn't this circular logic?  In terms of charge, a "closed system" is one in which charge can neither exit nor enter.  If the charge neither exits nor enters, then of course the sum thereof stays constant.
Or is the principle saying that the only way for the sum of charge in a system to change is via transfer of charge in or out of the system?  (In this case, wouldn't it make more sense to state the principle as "charge can neither be created nor destroyed"?)
 A: You're right that it's a bit circular as stated.  The more rigorous way to state a conservation law is something like:

The rate of change of [quantity] in a bounded system is equal to minus the rate at which [quantity] leaves through boundaries of that system.

A "closed system" is then a system for which both of these rates are zero, i.e., the [quantity] is not moving through the boundary of the system.
The version you propose, "[quantity] can neither be created nor destroyed", is closer to this more rigorous statement.  But the rigorous statement is a bit stronger than this.  If a charge were to suddenly teleport across the room, without passing through the points in between, this would satisfy your version of the statement;  but it would not satisfy the rigorous version of the conservation law above.  Moreover, it's perfectly possible in particle physics for charges to be created or destroyed, so long as equal amounts of positive and negative charges are created or destroyed.  Your version of the statement would seem to outlaw these events, but the rigorous version does not.
A: These statements are not circular but equivalent, you can assume one is true and the other follows. That is:
if
A: A closed system is a physical system that does not allow charge transfer.

and

B: The algebraic sum of all the electric charges in any closed system is constant.

are true then we can conclude that:

C: Net electrical charge can neither be created nor destroyed.

Similarly, if A and C are true, we can conclude B.
This is similar to geometry, where you can either postulate the existence of parallel lines and then prove that the sum of angles in a triangle is 180°, or you can postulate that the sum of the angles is the same for every triangle and prove that parallel lines exist.
Circular reasoning is a fallacy which appears when someone is trying to prove a statement using an equivalent statement as assumption. This is not the case for the laws of conservation, which are postulated, not proven.
A: Yes, it is saying that the only way to change the sum of charge in a system is via transfer into or out of the system. "Charge can neither be created nor destroyed" is not strictly accurate, though. For instance, if a positively charged positron and a negatively charged electron collide, they can "annihilate," leaving behind uncharged photons. This doesn't change the net charge, but it does "destroy charges."
A: No, the definition is perfectly correct and not circular at all.
For example, consider the principle of "conservation of sound", which states that if no sound enters or exits a closed system, then the total amount of sound in that system is constant. That is false, because I can clap my hands. Sound is not conserved, even if you don't let any come in from outside, because you can make it. You can't do that with charge, so the statement is nontrivial.
A: You could imagine a theory of electromagnetism in which the charge of 'fundamental' particles in the theory (let's stick to protons) is allowed to change with time. In these types of theories, closed systems do not have the property that the net charge within them is constant. The principle of conservation of charge is a statement that says that no such theories can describe reality as we observe it. 
Your last paragraph is correct in that the principle of conservation of charge does imply that the only way for the sum of charge in a system to change is via transfer of charge in or out of the system. This does not preclude processes in which, for example, we may have a neutral particle decay into a positively charged particle and a negatively charged particle (in practice, beta decay), so the statement "charge can neither be created nor destroyed" depends a bit on what exactly you mean by 'created' and 'destroyed'. 
