Is it necessary that a capacitor stores energy but not charge? Is it necessary that a capacitor stores charge? The definition of capacitor given in books is that it store electric energy. So is it possible that the capacitor does not store charge but stores energy only? 
 A: If you'll take some time to search this site for capacitor related questions, you'll probably find that I and others have often pointed out that capacitors store energy and not electric charge.
A charged capacitor has stored energy due to the work required to separate charge, i.e., the plates of the capacitor are individually charged but in the opposite sense ($+Q$ on one plate, $-Q$ on the other).
Yes, you'll often read phrases like "A capacitor stores electric charge". This is just plain wrong.
However, you'll also read phrases like "$Q$ is the charge on the capacitor". Literally, this is wrong. However, as long you understand that $Q$ is the charge that has flowed from one plate to the other, you'll stay out of trouble.
Bottom line, a charged capacitor is electrically neutral (in 'normal' operation). To say that a "capacitor is charged" is to use charged in the same sense as when we say that a "battery is charged". We mean that there is energy stored.

Given the good natured push-back in the comments, I thought I would do a quick Google search. So, for what it's worth...

A: It depends on what the capacitor is used for:  


*

*In some cases it is indeed a way of storing energy, similar to the battery. It however allows for higher transfer of this energy, although a rather short storage time.

*Capacitors may be used as a way of creating high electric fields. In this case the potential difference between the plates is more crucial than the energy involved.

*Finally, by far the most frequent use is in $LC$-circuits, that are part of any generators/receivers of the electromagnetic waves of radio and tv frequencies. In this case the charge is probably the most important variable.

A: To put my thoughts into an answer instead of comments, it depends on what you mean by "store charge". If you mean "is there a net charge stored across the entire capacitor", then this is not correct. However, if by "store charge" you mean "there is excess charge stored on each plate", then you would be correct. Of course, the issue is that some people might take "store charge" to mean the former and not the latter case, so it is less confusing to say "capacitors store energy"$^*$, or as Khan Academy puts it: "capacitors store an imbalance of charge".

$^*$Of course, you need excess charge "stored" in certain locations to allow for this energy to be stored in the first place ;)
