Time travel

Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space, either sending objects (or in some cases just information) backwards in time to some moment before the present, or sending objects forward from the present to the future without the need to experience the intervening period (at least not at the normal rate). Any technological device that is used to achieve time travel is commonly known as a time machine (タイムマシン). Time travel is present in some media related to the original Mega Man series (involving the Mega Man X series in two of them) and in the game Rockman.EXE Operate Shooting Star.

Mega Man II
In Mega Man II, Dr. Wily uses a time machine (named Time Skimmer in the US and European manuals) to travel to the future. Before the events of the game, Dr. Wily learns of a top-secret project to create an experimental time-machine known as the Time Skimmer at the Time-Space Research Laboratory (Chronos Institute in US and European manuals). He proceeds to steal it, originally planning to use it to change the past, but Wily discovers that the time machine had a serious flaw and could only travel into the future and back. Wily uses it to travel approximately 37.426 years in the future. While in the future, he experiments with the technology of the age and reprograms the future version of Mega Man, taking him back to his own time and renaming him Quint.

Mega Man: The Wily Wars
In Mega Man: The Wily Wars, Dr. Wily build himself a time machine and uses it to travel to the past and revived his robots from Mega Man-Mega Man 3. To stop Dr. Wily, Dr. Light hastily created a time machine to send Mega Man to the past.

Rockman & Forte: Mirai Kara no Chousensha
The antagonist of Rockman & Forte: Mirai Kara no Chousensha, Rockman Shadow, came from the future by unknown means.

Rockman.EXE Operate Shooting Star
The NetNavi ClockMan.EXE has the power to travel in time.

Rockman ×over
Villains from different periods confined Mega Man in a gap between the space-time. Without Mega Man to solve the crisis, Dr. Light and Dr. Cossack mass-produced a new Reploid named OVER-1 and sends them to different periods.

By gathering rare materials (Map Parts), Dr. Light will invent a "Space-Time Moving Machine" (時空間移動マシン) that allows OVER-1 to travel in space-time with the Flutter and fight against Master Bosses.

Mega Man (Ruby-Spears)
In Ruby-Spears' Mega Man animated series, Dr. Light created a time machine in the episode Future Shock. Dr. Wily discovers about it and attacks Dr. Light's laboratory to steal it, but is stopped by Mega Man. During the confusion, Mega Man believes Dr. Light was lost in time when he entered the machine, which returned empty, and Mega Man travels with Rush to the future to search for him, without knowing he had not entered the machine. In the future, Wily was able to conquer the world because of Mega Man's absence, and the time machine is taken from him. He discovers Dr. Light was not lost and manages to recover the time machine, returning to his time.

In the episode Mega X, the Mavericks Vile and Spark Mandrill travel to the past with a time portal to obtain Litanium, and X also travels back in time to stop them.

Mega Man: Upon a Star
In the OVA Mega Man: Upon a Star, Dr. Light created a time machine in the second episode, Wish Upon a Star, to help Mega Man. However, Dr. Wily discovered about the time machine when he was accidentally sent to Dr. Light's laboratory, and steals it to help in his evil plan. Mega Man damaged the time machine to stop Dr. Wily from using it, and recovers it in the end of the episode.

In episode 3, Future Beware, Dr. Light fixed the time machine. As Dr. Wily is hiding in Japan, Mega Man, Rush and Roll use it to travel one year in the future to discover what he is planning to do. When they arrive, Japan was completely destroyed and they return to escape from Wily's forces. Mega Man than decides to travel one month at time, and discovers that Dr. Wily plans to destroy Japan with a typhoon. Mega Man succeeds to stop the typhoon, but the time machine is destroyed when Roll uses it in an attempt to help Mega Man.

Mega Man (Dreamwave Productions)
In the last issue, X uses a small time travel device to return to the past and talk with Dr. Light.

Mega Man (Archie Comics)
In issue 20, sometime between the events based on Mega Man 3 and Mega Man 4, Dr. Wily takes over a time travelling device in the Chronos Institute and travels 40 years to the future to meet his future self. However, he inadvertently sends Mega Man to random time periods, most being events that will happen in the future.

The events Mega Man is sent to are Ra Moon's betrayal (Super Adventure Rockman), Mega Man's battle against Gamma (Mega Man 3), battle against Quint (Mega Man II), Dr. Cossack's defeat (Mega Man 4), the first battle against Terra (Mega Man V), The First Annual Robot Tournament (Mega Man 6), Bass's first appearance (Mega Man 7), Duo falling on Earth (Mega Man 8), King attacking a museum (Mega Man & Bass), meeting Quint again (or a similar robot), a fight against Splash Woman (Mega Man 9), and the Roboenza (Mega Man 10). Dialogue throughout the journey suggests that the events of the comic occurred after the fight with Gamma, but before encountering Quint.

In the Dawn of X story arc, Xander Payne utilized prototype Time Skimmer technology at the Chronos Institute to travel through time. He intended to travel to the past in order to stop the Robot revolution before it ever occurred, although he ends up traveling to the future instead. He witness a ton of events including Mega Man's battles against the Wily Walker, Gamma (MM3), and Quint (MMII), Dr. Wily encountering an individual who claims to have known him longer than he could imagine, Mega Man and Bass shooting at the time anomaly, and Mega Man working together with Sonic the Hedgehog to battle Tails Man (Worlds Collide), before finally stopping at a time before the first Mega Man X game. There, he encounters X and the Maverick Hunters battling a recently re-activated Wily Walker. He mistakes X for the Mega Man he knows of, and believes that he led a robot revolt. X tells him to calm down, and recognizes him as a member of the Emerald Spears, who were still around at this time. Xander is then escorted by X to safety, and is told about the concept of Mavericks. He is then taken back into the time stream, and returned to the present, just a few moments after he left. He is then arrested and jailed. In his cell, he carves pictures of what he saw, including many Xs and infinity signs, the helmets of Mega Man and Bass, and the head of Sonic. As he does so, he babbles on about saving everyone, no matter how many lives it takes, and that worlds will collide again.

Rockman World 2
In the Rockman World 2 manga, which is based on the game, Dr. Wily uses a time machine to capture Mega Man in the future and change him into Quint.

Rockman.EXE Stream
ShadeMan travels to the past and tries to conquer the world with Darkloids.

Trivia

 * The names "Time Skimmer" and "Chronos Institute" and the approximate time Wily travelled (37.426 years) are used only in the USA and European instruction manuals from Mega Man II. They are unnamed in the Japanese version, and no approximate time is given to how many years Wily travelled into the future.
 * Chronos is a Greek personification of time.