Origin (Counter-Earth Rikki)
Rikki Barnes was the sidekick of Captain America in the Heroes Reborn world. She was raised by her grandparents, Richard 'Bucky' Barnes and Peggy Carter Barnes. She was a always a good kid who loved dance. She dreamed of attending Julliard in New York City to study dance, but could not get a scholarship. She had a brother named John, who joined the World Party, a group of Neo-Nazis lead by Master Man and Red Skull. John strapped Rikki to a missile and was going to launch it when she was saved by Captain America.
There are two versions of Rikki Barnes. The first one is referred to as "Counter-Earth Rikki", whom was created by Jeph Loeb and Rob Liefeld. She first appeared in the special Heroes Reborn issue ½ (1996) before starring regularly in Captain America Volume 2. The first Rikki Barnes remains on Counter-Earth with her world's version of the Young Allies.
The second version of Rikki Barnes, referred to as "Onslaught Reborn - Rikki" was also created by Jeph Loeb and Rob Liefeld. She first appeared in Onslaught Reborn issue 1 (2007). This version has been on Earth-616 for some time and would become known as the new Nomad. She also joined a band of heroes known as the Young Allies, but died during the "Onslaught Unleashed" event.
Major Story Arcs (Counter-Earth Rikki)
Partners with Captain America
After meeting Captain America, she was given a costume and trained by SHIELD and Captain America himself to become his sidekick. She always had a feeling that she did not belong. According to SHIELD files, she is a chronal anomaly and should not exist. When Captain America and Falcon left Rikki's world to return to their own she didn't understand why she was being left behind. Cap knew that she wasn't from their world so she had to stay there but couldn't explain it to her which just made her more angry. Feeling alone in her world Rikki found other allies and tried to protect her world when it seemed to go to hell there were earthquakes, floods, comet collisions, cities disappearing worldwide destruction. But then Doctor Doom arrived to 'save' them but for Rikki and the Young Allies the price was too high. Doom didn't want to fix things, he wanted to leave things as they were so he could better control the populace.
Vs. Doom & meeting the Thunderbolts
While Doom called it Planet Doom, others called it Counter-Earth and Rikki just thought of it as home. With help from Kid Colt's teleportation powers her and Toro came to Earth 616 to threaten Doom with a biological weapon if he didn't abdicate leadership of Counter-Earth. Doom actually enlisted the Thunderbolts who were being led by Captain America at the time in order to stop this act of eco-terrorism against the people of Latveria. While Captain America felt a little familiarity with her he didn't remember his time with her and believed it is possible she could do as she planned. Bucky and Toro had some problems with their mission but were willing to follow it through for the greater good and they held their own against the Thunderbolts. When Captain America arrived she couldn't decide if she wanted to hug him or smack him. When hostilities resumed she actually used his own shield to break open the bio-chemical weapon canister. She expressed her anger at the heroes abandoning her world leaving it easy pickings for the likes of Doom as she opened the canister. But the chemical weapon was inert, there was no way that she'd kill thousands of people she just wanted Doom to think she would. By Cap forcing her hand he called her bluff and Doom won which she expressed as she teleported back home.
Later, the Young Allies encountered the Thunderbolts on their home world, when a rift called the Void was threatening to destroy both worlds. During the crisis' climax the Thunderbolts where returned home, however Jolt, remained behind on Counter Earth and joined the team in continuing to stabilize and re-order their world.
With the Exiles
Recently, the Exlies visited Counter-Earth to save it from Proteus the reality warping mutant who had taken over the Exile's teammate Morph's body. At first, Proteus convinced the Rikki and the Young Allies to fight the Exiles, however Bucky later figured out the truth when Proteus was enjoying torturing the Exiles. Proteus seemed to be winning, but two cosmic entities known as "O" and "K" - who until them been working with the Young Allies, ripped Proteus away from the fight, saying that they've been waiting for him. They supplied Proteus with an army of nukes to decide the fate of the world.
Empress Dorma of Atlantis and Proteus clashed, resulting in Proteus taking Dorma's crown. He raised Atlantis up from the ocean floor, which killed the entire population. The Exiles arrived with the Young Allies at Atlantis. Proteus then launched the nukes. Luckily, Colt and Jolt stopped the nukes without detonating them. Proteus had the Exiles and the Young Allies easily on the ropes. Protus put his dislodged crown back on to gloat, however unbeknownst to him, Blink had rigged it with a behaviour modifier device which caused Proteus to believe he really was Morph, trapping Proteus persona in Morph's body. The Exiles then teleported back to Panoptichron and sent the last remaining nukes harmlessly into space. As they left The Young Allies thanked the Exiles for saving their world from the nukes, Dorma, and Proteus.
Rikki still lives on Counter-Earth battling that worlds problems with the Young Allies.
Note: Rikki's Earth-616 counterpart died at birth.
Origin (Onslaught Reborn - Rikki)
The Rikki Barnes of the Onslaught Reborn universe was different from Counter-Earth Rikki. While she had largely the same background and trained with Captain America, on this world's Rikki, the Heroes of the Heroes Reborn universe did not leave, so all the damage that happened when the world was moved from its pocket dimension did not happen.
Major Story Arcs (Onslaught Reborn - Rikki)
When Rikki encountered Franklin Richards running from Onslaught she summoned the Avengers who battled the monstrously, powerful entity. This Onslaught is not the same as the one before, being made of the mutant energy from the depowered mutants after 'M' Day. However, its goal of capturing Franklin Richards remained.
The fight against Onslaught would lead to the Baxter Building, where Rikki sacrificed herself to push Onslaught into the Negative Zone. Rikki died willingly but, instead of dying, she found herself on Earth-616 instead.
Transported to Earth-616
Hearing that her Captain America was dead, she felt lost again and clung to the only things she had, her heroism and her brother. While not technically her brother, she sought out John Barnes of Earth-616 and falsified an ID so she could go stay close to him. This John Barnes was actually a pretty nice guy so she pretended to be Rikki Baines his schoolmate and best friend. Rikki heard that there was a new Captain America and she desperately tried to meet him, not that she wanted to be his Bucky but maybe if they met....just maybe. However before she could meet him, she was intercepted by Black Widow who knew exactly who Rikki was and cautioned her about trying to meet Captain America who was in fact James Buchanan Barnes of this world.
The New Nomad
While in school she noticed several classmates acting odd and believed something was up but John felt she was just being paranoid. Bucky tried to investigate the school at night following the students but instead she found a wolf-man who injured her and ripped her suit. When she got back to her modest apartment (which she paid for by washing dishes in a restaurant) she found a brand new Nomad costume and a note that it was for her. The next day at a coffee shop with John she got up the courage to ask John about his family. It turned out that his mother died during childbirth giving birth to his little sister who also died, and his father died in a terrorist attack on Philadelphia. This was difficult for Rikki to hear about how she was never born but just then a bomb went off across the street. Flag-smasher was attacking a military recruitment facility. John was injured in the explosion but Rikki put on her Nomad costume to fight Flag-Smasher. She was aided by Falcon who she remembered but like the others who left the Heroes Reborn universe he didn't remember her. Rikki explained who she was and where she was from and Falcon suggested she continue being Nomad, whoever gave her the costume thought she could handle it. When John was released from the hospital Rikki visited him but he mistook her friendship for attraction and Rikki had to tell him she thought of him as a brother.
He was hurt and refused to speak to her and ended up turning to the people who were brainwashing the students at their school. Nomad investigated Desmond Daniels who the brainwashed students were supporting believing he was behind it. She was then attacked and taken prisoner by the wolf-man and mastermind behind it all. John finally became concerned when Rikki missed a few days of school while she was being brainwashed like the others though it was more difficult to affect her. They released her and had her reveal her identity to the whole school in support of the student council nominee the others were supporting. It turned out it was all a plot by the Secret Empire to test if they could influence voting by brainwashing specific members of different groups causing the masses to fall in line.
The Secret Empire wanted to shut down the experiment but Professor Power who was the mastermind behind it all was pretending to be a politics teacher at the school. Professor Power refused to shut the experiment down and allowed the entire school to riot. He intended to kill Nomad but she managed to escape and fight off the super-villain and his wolf-man henchman. The Young Avengers arrived to assist Nomad and the police with crowd control and diffuse the situation. However it was John that realized they were brainwashed to follow Desmond Daniels who was an innocent pawn, it was another student Matt Surman inciting the riot. Rikki got Desmond to talk the rioters down while John confronted Matt not knowing that Matt had a gun. Matt shot John and tried to shoot Rikki but her uniform protected her, John was not so lucky and he died. Later Rikki visited John's grave back in their home town of Philadelphia, she didn't blame Matt it was an unforeseen effect of the brainwashing. It was then that Captain America arrived and spoke to her for the first time. He said Barnes was a great name and that she shouldn't let this affect her duty because she'd make Steve Rogers proud. She asked if it was him that gave her the Nomad costume, he had assumed that she had made it herself. Meanwhile Black Widow had been watching the whole time and smiled suggesting it had been her.
With the Young Allies and Death
Eventually, Rikki met other young heroes who were trying to find their place in the world, and formed a new superhero group known as the Young Allies, together with Gravity, Arana and Firestar among others. She did a number of missions with the team, also teaming up with Captain America.
It was however then that disaster struck. The villain known as Onslaught had resurfaced again and during the battle that involved the Avengers and the Young Allies, Rikki Barnes was killed. She was mourned greatly by her fellow teammates. Note: the Rikki who became Nomad and lived on Earth 616 has died, the original Rikki Barnes from the Heroes Reborn event still lives on Counter-Earth, as can be seen above.
Rikki doesn't possess any real powers or even a super-soldier serum, she's just a natural athlete who has been trained by SHIELD and Captain America. She is a gifted fighter, marksman and acrobat with a certain degree of familiarity with technological devices of a SHIELD agent.
As Bucky, she wore a bulletproof costume modeled after the original Bucky. A vibranium-photonic, energy shield that allows her to absorb and reflect just about anything. Vibranium-soled boots that allow her to run up walls, move silently, leap greater distances than usual and land safely from great heights. She also often wielded a pistol.
As Nomad, she wears a bulletproof costume modeled after the Nomad identity once worn by Steve Rogers. She retains the vibranium-photonic shield and now uses throwing discs used by previous Nomads. It's possible she still possesses the vibranium-soled boots, though she no longer uses the pistol in her new identity.
All of this armor and weapons are now useless after all of Earth's excavated vibranium was deactivated in Doomwar.
Problem with this character
The Rikki Barnes now on 616 'Normal' Earth came there from the end of the Onslaught Reborn series. However the world that Franklin created in that series was a re-construction of the "Heroes Reborn" world some time after the heroes had come back home, thus when Captain America said he remembered training Rikki, he is actually talking about the one that is still on Counter-Earth not the one from the pocket universe Rikki comes from.
It is possible that Franklin took Rikki from Counter-Earth and reset her memories. But given he made new versions of everyone else, it seems unlikely.