Poseidon, God of the Sea - water powers
Zeus, God of lightning - lightning powers
Hades - God of the Underworld - devilish powers
But what about Ares? Is he good at fighting? Can he summon swords at will? What is a "war" power?
Well he's not a strategist, that's Athena.
I think it's fair to say Ares is a good fighter. But he's not the best- he's lost to Athena, and he has been on the losing side of a war as well. And that doesn't mean he's literally anything else - he runs in the face of battle, he sneaks around with Aphrodite behind her husband's back, he is hot headed and impetuous and bloodthirsty. He's a warrior who's a step above a barbarian(he represents the violent and bloody aspects of war), not a general (Again, that's Athena, she's not goddess of wisdom for nothing), or even a great warrior like Hercules, who did his Labours to atone for his crimes.
Ares is usually portrayed in a less than flattering light, and is frankly a bit of a bloodthirsty flake. Deimos and Phobos, Terror and Dread, are his attendants, without military strategies could be planned like chess strategies, because your men would never cut and run in the face of battle.
You could possibly extrapolate based on his children(Deimos and Phobos being the most commonly and closely associated with him), but he's not a DnD character. It's not a case of every god having a signature spell to summon something that represents them.
He doesn't exactly have a "power" like some of the other gods do. Zeus, Hades, and Poseidon have powers like that because they rule parts of the world, with Zeus as king of the sky, Poseidon ruling the oceans, and Hades as king of Erebus, or Hades, the Underworld. Ares isn't really portrayed as being very smart, he is very much a brutish, bloodthirsty warrior. He is a very good fighter, although he isn't good enough to win every fight. Like fifthviolet says, he's portrayed pretty negatively.He's a coward, and hates losing. He has a temper, and doesn't think before charging into battle. He has lost battles, but they were only to people who were smarter than him. In a fight of brute force, he could probably beat almost anyone.
So, yeah, he doesn't really have specific powers like Zeus and his brothers. I suppose he might have the power to make people want to start a war, but that's just speculation. If you need specific powers for some reason, like you're making a DnD character, he could have fire powers since he does have fire breathing horses, and fire can be rather consuming and destructive. Or he could just be an over powered fighter. Sorry if this was more than what you wanted and/or didn't really answer the question well. Hope it helped at least a bit, though!
I know this is a very old thread, but if anyone finds this in research or because they were curious, I have an answer:
I think of Ares with fear and rage manipulation of a sort. His sons, Phobos and Deimos, accompany him to battle, and they have control over terror, dread, etc. So maybe Ares does too?
In Percy Jackson and the Olympians (and wherever else he appears in the Riordanverse), he has some form of pyrokinesis (control of fire), but I think that's just kind of a fun creative liberty.
Since MythsMouse mentioned D&D, I would also like to add that Ares probably has some rage ability like that of a barbarian, making him stronger and more resilient, but less focused/observant. He may also be able to manipulate others' emotions (particularly rage, feeling of adrenaline, or even bravery) to make them enter a battle frenzy.
One last thing: I'm pretty sure that in the Iliad Ares screams with the strength/sound of nine thousand men. So maybe he could yell very loud when wounded or angered to stun and/or confuse opponents, perhaps even doing some sound-based damage. Sorry if I wasn't able to provide any ideas to people. I hope this helps those who read it!