The tv show Alcatraz features a time warp which causes everyone in Alcatraz in 1963, including its prisoners, to go forwards in time into 2012, and due to the fact these dangerous inmates from the past are loose, they must be recaptured.
Continuum is perhaps the best example of how to have a show that is about time travel, has very specific rules for how it works, but actually features very little time travel. In this universe, time travel works as such:
1. Time Travel only works in one direction (Backwards).
2. The instant someone travels back in time, the period they came from immediately starts erasing, and this process is impossible to stop, meaning the moment time travel occurs, every single person the time traveler knew is wiped from existence.
3. The time traveler's memory/existence is not effected by the changing of their timeline once they make the journey, even if a past version of them is killed.
Season's 1-3 focus heavily on the psychological toll this takes on the protagonists as they slowly take in the ramifications of only a single trip through time, and how You Can't Go Home Again. Season 4 goes Off the Rails when the villains finally figure out how to break these rules.
Doctor Who is about a time travelling, human-seeming alien and their human companions who travel throughout time and space in the TARDIS, a spaceship which is disguised as a blue London police box and is Bigger on the Inside. Although the show started with time travel on Earth just going to historical eras to see what happened in the past (as it was originally devised as an edutainment programme), later series would always have some alien interference in whatever was happening in the episodes set on Earth. While the Doctor firmly believes that the timeline should not be altered, some stories are concerned with the TARDIS team trying to prevent somebody else from changing the timeline.
Though this only seems to apply when the audience know what history "should" be. The Doctor won't save Pompeii from burning or steer the Titanic clear of the iceberg, but will happily stop a volcano erupting on the planet Tharg or a spaceship hitting an asteroid and exploding. The question "but what if the volcano on Tharg is *supposed* to erupt and kill everyone" is never asked. Bellisario's Maxim may apply here. The Doctor mentions in the new series that he can tell the difference between an event that can be changed and a fixed point in time which can't.
In fact, Doctor Who has generally been somewhat shy of actually using Time Travel as part of the plot, rather than merely a way of delivering the characters to the Adventure Towns of the week.
Until the Steven Moffat era. Moffat's episodes are well-known for incorporating Time Travel or temporal paradoxes as an integral part of their plots, and the season arcs in his years as executive producer have both focused on issues associated with the Timey-Wimey Ball.
In Life on Mars (2006) and its sequel series, Ashes to Ashes, when time travelers travel to the past, they are going to another world. In the series, victims of trauma, such as people in comas or even people who are dead, are transported to limbo, which is set in the year of ones source of trauma, and allows them to get a chance to lay their demons to rest by confronting past problems, which then allows them to ascend into heaven.
However, Life on Mars (2008) does something radically different, with time travelers being astronauts going to Mars using an advanced full sensory simulation program which allows them to digitally leap through time, with the inhabitants of the different times being A.I, and some of them resembling people the traveler knows in the real world. The series was still well received, but many fans of the series found this twist upsetting.
In Quantum Leap, highly intelligent protagonist Sam Beckett invents a machine which allows him to travel through time and jumps into it after his program is threatened to be shut down. He finds himself jumping through time, and with interesting rules and constraints.
1: Whenever he jumps through time, his consciousness and memories are actually the only parts of him to time travel, meaning whenever he time travels, he inhabits someone elses body, whos mind is then sent into Sams body in the future, however, Sam leaves the body he is in after one week into another one and allows the original mind of the body to return to it from the future.
2: He can only travel within his lifetime. Meaning he can only travel between when he was conceived and when he entered his time machine. Since he was conceived in 1953, he cant travel back further than that year. However, later in the series, Sams friend Al transfers his genetic code to Sam, allowing him to travel further back than 1953, his new limit being 1932.
3: His leaps through time arent controlled by him. His trips are controlled by a higher power so to speak, and the bodies he inhabits arent randomly chosen to host his mind, but actually require help with their personal life.
In Seven Days, the hero was the only one who could work the device reliably, and he could only go back seven days at a time.
Sliders had an interesting variation: The title characters dont travel through their own world, as their portals always lead them to a parallel Earth during the current year. However, one such world is a place where events play out exactly the same as they did on the Sliders' earth, but at a much slower rate, so when the Sliders' arrive, it seems to them be more than ten years earlier.
In the original Star Trek, time travel required either a dangerous and complicated slingshot maneuver or a precision jump into the Donut of Forever or Mr. Atoz's Atavachron, but these days Trek characters can travel through time by spilling coffee on their tricorder. (Which is probably why Star Fleet now has a department of time travel cops staffed entirely by grim-jawed Men in Black, as seen in DS9.)
Note that this isn't just a Plot Tumor (though it is one of those too)- time travel really is getting much easier in-universe as technology advances. By the end of the 24th century, it's shown, Starfleet's temporal function is beginning to overtake its spacial one. This is a large part of why they went to Prequels after Voyager. Of course, the Plot Tumor in question being TIME TRAVEL, this helped not at all.
Time Travel is such an amusingly big thing in Star Trek that, in Star Trek Online, Section 31 are revealed to have a star system set up specifically for pulling off the "slingshot around a star" stunt with precise calibration.
In Terra Nova, people are able to go back in time through an accidentally created hole in space-time. However, travel to a different time takes one to a different time stream (a.k.a another universe), allowing them to travel without messing up history.
In The 4400, people in the future have advanced technology that allows them to pull people out of their place in time an put them in another, they can also give superpowers to them as well.
Timeless starts with a group of criminals stealing a secret time machine (called the Mothership) from Mason Industries in order to change past events. Mason Industries then informs the government of the existence of time travel. The NSA quickly recruits a historian, a soldier, and the remaining time machine pilot to use the prototype machine (called the Lifeboat) to go back and keep the bad guys from altering the timeline. As a rule, they fail at least in some way, so every time they come back, they hit the Internet to see how things have changed. As it turns out, the "bad guy" is actually trying to erase an Ancient Conspiracy from history using the notes that are yet to be written by the above-mentioned historian. Oh, and there are personal consequences to time travel as well, as the historian finds out that, after their first jump, she no longer has a sister, who was never born in the altered timeline.
In Time Trax, the method varied, but the rules were that you could only travel between two set time periods (The Present and The Future), and more than two trips in a lifetime are lethal.
The series Voyagers! centered around a time traveler and a young boy who travel through time trying to fix things that went wrong in history.
Heroes has the character Hiro, his time travelling basically set off the whole first series in an attempt to change the future, it's a lot harder than you imagine, apparently. Also in the second series, he travels back in time and creates the character he heard in his bedtime stories. Peter also is prone to time travel but less often.
Kamen Rider Den-O features a superhero that travels back through time on a passenger train, DenLiner. Fairly early on, it is established that he is a "singularity point" a person who is completely immune to changes in the time stream and thus especially qualified to battle time-traveling Monsters of the Week. Why the OTHER singularity point handy, Hana, doesn't do the job remains unexplained.
She doesn't do it because Hana is not part of the timeline, she's from a deleted timeline and is the only reason the characters know time has been changed.
Lost from season 3 on, but especially in season 5. In Lost time travel nothing can be changed and everything is one huge Stable Time Loop. Note that the first person who claimed that time could be changed was fatally shot by his own mother before he was born once he actually tried to.
Odisea Burbujas using Professor Memelovskys Time Slide in most of the episodes, as a way to teach childrens history as it was an educational show.
Prehistoric Park: A group of people (lead by Nigel Marven) set up a safari park filled with prehistoric creatures by traveling to the past and capture the creatures themselves. The time traveling device itself is never discussed in depth but it is what made the whole thing possible.
Star Trek: Enterprise: One of its central premises was a "temporal cold war", in which bandits are going back in time and messing with the timeline. The rules and limitations of time travel are never explained to anyone at any time, so the writers had a license to Ass Pull.
Voyagers! - this was the entire premise. The 'Voyagers' were charged to Set Right What Once Went Wrong - they used one gadget, the Omni (which looked rather like a large gold pocketwatch), both to travel and to figure out what was wrong and how to set it right.
Lois & Clark had a few time travel episodes that included Time Machine author H. G. Wells.
With the pitted combatants sometimes in different time periods, Deadliest Warrior obviously uses this in their simulations. However, the most notable case is in Jesse James vs. Al Capone, where Jesse and his men seem to suddenly spawn in a museum during the Depression and proceed to break out the museum pieces rather than being armed from the start like most fights.
Lost hinted mildly at time disparity in season 2, flirted with time travel in season 3, and took the full plunge by the end of season 4.
Nick Arcade had a Time Travel board where the player (Mikey) moves between the past and the future of his own neighborhood.
Power Rangers occasionally calls on this, even outside the Time Force season. Mighty Morphin' had a couple of trips back to the wild west era and the quest for the Zeo Crystals. SPD team had two separate time travel eps so they and the Dino Thunder Rangers could each visit the other team's home turf. Cam did the Kid from the Future thing on his quest to become Sixth Ranger, and Carter got the chance to repeat a day and save the lives of his teammates.
In season 2 of Roswell, Max travels back in time after everyone but he and Liz dies, in order to persuade past-Liz to break up with past-Max and make him get together with Tess. It's very silly and involves mariachis.
Stargate SG-1 had several episodes involving time travel—"1969" when they travel back to said year due to Stargate mishaps, "Groundhog Day" Loop episode "Window of Opportunity", "2010" showing a possible future where everyone is sterilized, "It's Good To Be King" with prophecies from the Ancient time-travelling puddle jumper, season-8 finale "Moebius" involving the same jumper and a twisted Time Loop (to be expected given the name), and season 10 Grand Finale "Unending".
1. Travelling through a wormhole that intersects with a solar flare causing the wormhole's course to alter sending the matter in transit back to either the dialing Stargate, the destination Stargate or another Stargate altogether.
2. Using a time machine built by the Ancients to either get an area of a galaxy stuck in an ever repeating loop, or a Puddle Jumper with a time machine component that can only jump in jumps of 100+.
3. Although not time travel per se, but, Asgard time dilation fields can be reversed to the time when the field was created.
Supernatural - Sufficiently powerful beings (e.g, angels) are capable of time travel, though it's not used often and changing the past was supposedly impossible until the Screw Destiny at the end of season five. In season six, Balthazar rewrites history by saving the Titanic; the incarnation of Fate, already ticked at the main characters for putting her out of a job, draws the line at changing the past and coerces Castiel and Balthazar into fixing things.
Lovecraft Country: In "Rewind 1921" Montrose, Leti and Atticus travel back to Tulsa in 1921, when the Tulsa massacre occurred (which Montrose survived, while most of his loved ones didn't).
Cinderella Chef: One of Ye Jia Yao's customers created a time machine, and she uses it to travel back to ancient times.