Judged mainly by how magic is used in stories and game-systems that explain them, you could probably make a decent story-independent definition of magic as ‘Energy capable of containing and/or processing information’  
You could, if you wanted, build some pretty decent generic rules out of that and some assumptions about the physical (and meta-physical) properties of a specific world.  
The rules will be broken in all but the most defined magical worlds, because it’s so tempting for a writer to do a cop-out like ‘but it doesn’t work like that, because I say so’ to prevent an inconvenient ‘solution’ (if you give your anti-hero character a gun, it’s hard to explain why they don’t shoot the bad guy, if you give them magic you just wave your hands and mumble something about corruption and not being able to use magic to kill) but at least you’ve got the rules ready for your head-canons.

@Eeveeinheat  
Careful there, you’ll be accused of being an idiot and not understanding spells if you keep talking like that.

“rarity why is your magic on my horn??”  
“and why am I flying?”  
“and upside down?”

@Elric of Melnipony  
I’ve always wondered why they couldn’t create food of out air. Air isn’t nothing, and I can’t see why magic couldn’t change the number of protons, electrons, and neutrons of the atoms in the air, and then rearrange the molecular bonds, and then change the vibration of each atom and molecule to create perfectly cooked and yummy food. They do things that realistically would take about the same amount of energy, like transforming things from humans to smaller animals, and teleporting multiple people thousands of miles.

@Background Pony Number 17  
I was trying to keep it simple for the guy who couldn’t understand the two spells in the first place.

@Elric of Melnipony  

 
The two spells aren’t true opposites. “Expelliarmus” is a transitive spell; its effect (pushing something away) is upon another person. “Accio” is an intransitive spell; its effect (pulling something toward) is upon yourself.

@NounVerb  

 
But there are rules. Such as not being able to create food out of nothing.
 
 
@NounVerb  

 
What’s the difference between pushing and pulling?

@NounVerb  
Well, Expelliarmus is just for disarming, while Accio anything seems basically a fetching spell.
 
I’d say it’s possible one was developed independently of the other, and are both situational.

@PonyPon  
But they’re both ways of moving a wand. It’s the same spell with the same target, just moving in different directions. I just don’t see any reason for a completely different set of words to the spell.
 
My point is that, while there is a system (which is a good thing), several very visible aspects of it seem weirdly arbitrary.
 
In Fate/Stay Night, for example, characters use words and phrases in other languages, like Latin and German, for spellcasting. This is because casting a spell is more like triggering an internal change of state, and this internal change goes out and affects the world through the use of mana. It’s more like a self-hypnosis trigger word, so the actual words chosen are arbitrary and can be very different depending on which mage you’re talking about.
 
There’s a clear, simple explanation for any weirdness or differences in how the characters use verbal magic, and how they are able to cast simpler spell without an audible verbal trigger.

@NounVerb  
One is slapping the wand away, the other is grabbing it?

@Elric of Melnipony  
The Harry Potter books are sort of lax with showing this. The rules are vague. What’s the difference between Expelliarmus and Accio Wand, for example?
 
They do show that you have to learn how to use magic in order to do it effectively, at least.
 
Other good examples are of the Fate visual novels (and to a lesser extent, the animated adaptations), the Dresden Files, and Death Note.
 
Look here for more examples: http://tvtropes.org/pmwiki/pmwiki.php/Main/MagicAIsMagicA
 
 
@CogWeaver  
That’s a shitty way to write a story.

Okay, Sweetie Belle, here’s your first lesson on how magic actually works:  
Let’s start off by discussing what a ‘Deus Ex Machina’ is……

@martianmister  
Even magic has to have rules. The Harry Potter books are a good example of this.

@FanOfMostEverything  
I don’t think it’ll completely replace Pinkie Pie telling Twilight Sparkle “you still gotta explain”, but I do believe it’ll be useful, yes. Like with bad fanfics that casually handwave hoofwave away things that should still make sense regardless of magic being involved or not…

But then it would be science fiction, not magic.

Well, I can see this getting some use.

We ain’t gotta nor gonna explain shit.

So much this.