Time Travel is the ability in which an individual or object literally moves through different points in time.
A select few methods that make time travel possible exist on or in relation to Sonic's World, such as the Little Planet, where time travel can be performed through use of Time Warp Plates. In addition, the planetoid is homed to the seven Time Stones, which can allegedly grant the user complete control over time itself. At some point in the past, Dr. Eggman attempted to obtain these seven stones, but was stopped by Sonic, who utilized the aformentioned warp plates. (VG: SCD)
A mysterious entity known as the Time Eater possessed domineon over space and time. Eggman once took control of the creature so that he, along with his past self, could alter history to change all of his previous defeats by Sonic into victories. Their plan was thearted by Sonic, who had also teamed up with his past self. (VG: SG)
The most noteable individual to utilize time travel is Silver the Hedgehog, who has travelled to the past on multiple occassions in an effort to change his constantly-ruined future timeline. (SU: #75)
Silver's various methods of time travel are largely unknown, though in recent times, he has used the Genesis Portals, holes in space and time brought about by the failed reversal of the Super Genesis Wave. Other individuals have used these portals, most noteably the evil Reploid Sigma, whom hailed from Mega Man's world in the distant future. (SU: #76, #76)
Those who travel into the past are capable of altering their respective present day timeline by initiating any event that would have a large enough impact on future events. In most of these instances, the time traveller who initiated these changes are shown to have retained their memories of how their timeline used to be. Silver, during his travels, has caused this to happen to his timeline many times. Xander Payne also accomplished this feat, by using a Genesis Portal to completely abort an alternate timeline inwhich Sigma fused Sonic's and Mega Man's worlds. (VG: SRiv2, MM: #52)
While not strictly the same as travelling through different points in time, one of the known capabilities of the reality-warping Genesis Wave is making a reality excell forward through its timeline. When Dr. Eggman and Dr. Wily launched the second wave on their respective worlds, the timeline of Wily's home dimension of Earth 20XX had skipped forward by an unknown amount of time. MM: #24)