The Nine have greater power the closer to Mordor they are, also they get stronger as the more Sauron grows in power. (Sauron can even enhance them with some additional power like he did during battle of Pelennor Fields.) Gandalf in book says:
The Ringwraiths are deadly enemies, but they are only shadows yet of the power and terror they would possess if the Ruling Ring was on their master's hand again."
Far off in the North they used stealth and evading tactic on purpose, rarely they engaged in combat to not attract attention of their enemies, specifically White Council members and powerful elf lords.
From their origin we know they were warriors and sorcerers even before turning to wraiths (thanks to the Nine Rings of Power). Incapacitating fear aura and venomous Black Breath affecting all living beings in their presence are indeed stated to be their greatest weapon but they are also agile and fast without horses (of course without them they would be crippled and their ability to travel would be limited), also they can't be destroyed by normal means and every weapon that touches one would wither:
[...] they rushed towards him. Desperate, he drew his own sword, and it seemed to him that it flickered red, as if it was a firebrand. Two of the figures halted. The third was taller than the others: his hair was long and gleaming and on his helm was a crown. In one hand he held a long sword, and in the other a knife; both the knife and the hand that held it glowed with a pale light. He sprang forward and bore down on Frodo."
"Look!" he cried; and stooping he lifted from the ground a black cloak that had lain there hidden by the darkness. A foot above the lower hem there was a slash. "This was the stroke of Frodo's sword," he said. "The only hurt that it did to his enemy I fear; for it is unharmed, but all blades perish that pierce that dreadful King. More deadly to him was the name of Elbereth."
In the same time they were slightly intimidated by the presence of blade from Barrow Downs "with spells for the bane of Mordor" which were specifically designed to harm wraiths. But Witch-king who is "in many ways more powerful than others" was able to fulfill his goal. (Meaning stab ringbearer with Morgul-knife which would turn the hobbit into an obedient wraith under their command, and thus would bring them the Ring on his own.)
Also Aragorn did not defeat them in a normal sense, the Nazgûl retreated themselves and the fire used by Aragorn and hobbits affected only their ability to perceive the world bringing light to disperse shadows. (That's why they fear those who wield fire cause it places them at disadvantage):
A shrill cry rang out in the night; and [Frodo] felt a pain like a dart of poisoned ice pierce his left shoulder. Even as he swooned he caught, as through a swirling mist, a glimpse of Strider leaping out of the darkness with a flaming brand of wood in either hand. With a last effort Frodo, dropping his sword, slipped the Ring from his finger and closed his right hand tight upon it.
This next passage explains some of their later actions before Rivendell, they didn't also expected this particular "magic resistance" hobbits have. (The wound from the knife would subdue even powerful human warrior very quickly as the power of rings too would):
"I think I understand things better now," [Strider] said in a low voice. "There seem only to have been five of the enemy. Why they were not all here, I don't know; but I don't think they expected to be resisted. They have drawn off for the time being. But not far, I fear. They will come again another night, if we cannot escape. They are only waiting, because they think that their purpose is almost accomplished, and that the Ring cannot fly much further. I fear, Sam, that they believe your master has a deadly wound that will subdue him to their will."
The Fellowship of the Ring, Book 1, Ch 12, "Flight to the Ford"
Gandalf was able to hold his position against them at Weathertop using his power and still it was hard for him he said he was "hard put to it indeed: such light and flame cannot have been seen on Weathertop since the war-beacons of old.
"At sunrise I escaped and fled towards the north."
The actual abilities they possess:
"I was too careless on the hill-top," answered Strider. "I was very anxious to find some sign of Gandalf; but it was a mistake for three of us to go up and stand there for so long. For the black horses can see, and the Riders can use men and other creatures as spies, as we found at Bree. They themselves do not see the world of light as we do, but our shapes cast shadows in their minds, which only the noon sun destroys; and in the dark they perceive many signs and forms that are hidden from us: then they are most to be feared. And at all times they smell the blood of living things, desiring and hating it. Senses, too, there are other then sight or smell. We can feel their presence – it troubled our hearts, as soon as we came here, and before we saw them; they feel ours more keenly. Also," he added, and his voice sank to a whisper, "the Ring draws them."
Some sorcery also is their weapon:
Then the leader, who was now half across the Ford, stood up menacing in his stirrups, and raised up his hand. Frodo was stricken dumb. He felt his tongue cleave to his mouth, and his heart labouring. His sword broke and fell out of his shaking hand. The elf-horse reared and snorted.
With single gesture Frodo is disabled as if with some paralyzing spell and his sword is shattered at distance.
They definitely too have necromantic powers:
In notes on the movements of the Black Riders at that time it is said that the Black Captain stayed [in the Barrow-downs] for some days, and the Barrow-wights were roused, and all things of evil spirit, hostile to Elves and Men, were on the watch with malice in the Old Forest and on the Barrow-downs.
Unfinished Tales, "The Hunt for the Ring"
It was at this time that an end came of the Dúnedain of Cardolan, and evil spirits out of Angmar and Rhudaur entered into the deserted mounds and dwelt there.
The Witch-king as a powerful sorcerer shows the ability to cast a "blasting spell":
Over the hills of slain a hideous shape appeared: a horseman, tall, hooded, cloaked in black. Slowly, trampling the fallen, he rode forth, heeding no longer any dart. he halted and held up a long pale sword. And as he did so a great fear fell upon all, defender and foe alike; and the hands of men dropped to their sides, and no bows sang. For a moment all was still.
The drums rolled and rattled. With a vast rush Grond was hurled forward by huge hands. It reached the Gate. It swung. A deep boom rumbled through the City like thunder running in the clouds. But the doors of iron and posts of steel withstood the stroke.
Then the Black Captain rose in his stirrups and cried aloud in a dreadful voice, speaking in some forgotten tongue words of power and terror to rend both heart and stone.
Thrice he cried. Thrice the ram boomed. And suddenly upon the last stroke the Gate of Gondor broke. As if stricken by some blasting spell it burst asunder: there was a flash of lightning and the doors tumbled in riven fragments to the ground.
Also his ability to use a flaming sword:
The Black Rider flung back his hood and behold! he had a kingly crown. The red fires shown between it and the mantled shoulders vast and dark. From a mouth unseen came a deadly laughter.
"Old fool!" he said. "Old fool!" This is my hour. Do you not know Death when you see it? Die now and curse in vain!" And with that he lifted high his sword and flames ran down the blade.
It is also in their power to "inspire" their servants to fight better, mentally influencing them as well as inducing fear in enemies:
"Some said that it could be seen, like a great black horseman, a dark shadow under the moon. Wherever he came a madness filled our foes, but fear fell on our boldest, so that horse and man gave way and fled. Only a remnant of our eastern force came back, destroying the last bridge that still stood amid the ruins of Osgiliath."
"They have paid dear for the crossing, but less dearly then we hoped. [...] They swarmed across like beetles. But it is the Black Captain that defeats us. Few will stand and abide even the rumor of his coming. His own folk quail at him, and they would slay themselves at his bidding."
Standard equipment seems to be swords, glowing enchanted Morgul-knives and some darts with potent poison.