"Aaron, I'm standing at the Time Portal, which scientists say follows Terminator rules, that is, it's one way only and you can't go back. This is in contrast to, say, Back to the Future rules, where back and forth is possible, and, of course, Timerider rules, which are just plain silly."
With the Back to the Future-type machine, one simply gets into a vehicle of some sort, and the vehicle is transported to a certain time. When a traveler wants to go back, they use the machine again. This is pretty much the most common type, possibly having to do with the fact that one of the earliest time travel stories (The Time Machine) used this type.
A TARDIS-type machine works like a Back to the Future-type one except not only can you program it to go anywhere in time, but also anywhere in space. Basically it's a vehicle that can go anywhere in 4 dimensions.
Terminator-type machines usually involve some sort of big device that projects a traveller back, but does not come with them. Once back in time, the person has no way back to the future besides The Slow Path, unless they can somehow build another device, or if they were able to bring an entire additional time machine with them to leave behind on that trip also. (And this is sometimes precluded by time machines being too big, or the rules not allowing you to take things, or just time machines, with you.) Sometimes these only allow backwards trips to start with.
Time Cop-type machines are a cross between the Back to the Future-type and the Terminator-type; the traveller is sent back by a machine that does not come with him, but has some sort of way (such as a remote or prearranged time portal) to make a trip back, utilizing the future time machine. Can also being used as a "time scoop" to bring things from the past into the present without going there. Losing the signaler or missing the prearranged portal can require past travelers Writing Back To The Future to get home.
A Time Portal provides a direct gateway between two points in space and time is another variation. These can be random, appear and disappear in a predictable way, or be permanent. A pre-existing Time Portal is a way to introduce Time Travel to a series without opening the Pandora's Box of "why didn't they just go back in time and stop the bad guy".
A Time Dilation Field is a device that causes time inside a certain area to either go faster or slower. While not a time machine in the classical sense, a field with time set to go slower is a good way to travel forward in time.
In Real Life, Time Dilation is an actual effect that occurs when bodies are moving at different relative velocities, or at different depths in a gravity well. This is generally too tame and prosaic for all but the hardestScience Fiction, though.
There were a couple of Super Golden Crisp commercials in 1993 where Granny used a weird-looking magical clock to pull a "Granny Goodwitch Time Switch" to travel into the past to try to get away from Sugar Bear, like this one. Unfortunately, he was always a step ahead of her.
Homura of Puella Magi Madoka Magica has a magical buckler that allows her to travel back in time, but only as far back as her first meeting with Madoka because of her wish, making it a variant of the Terminator style of time travel.
The time machine in Meanwhile is one-way and can only go as far back as when its receiving end was originally built. When Timmy first encounters it, the Professor has locked it so that it can only go a maximum of ten minutes into the past.
Dale and Stacey Yorkes from the Marvel comic Runaways pilot a stationary two-seater TARDIS-type time machine.
In Suske en Wiske (Spike and Suzy) the "teletimemachine" is a Time Cop-type; the machine does not come with the time traveler, but an operator who stays behind can retrieve the time traveler at any moment. This feature was often used for last second rescues.
Summary: The time machine is a box containing a volume that exists over time. Turning the box on causes this volume to (slowly) dissociate from the rest of the universe, and turning the box off reverses that. Within this mini-universe, time flows like it usually does, but it cycles back and forth between the two endpoints - inside the box, time reverses when the box is turned off, and back again when the box is turned ("back") on. Turning the box on, waiting a minute and getting into the box just before it turns off, and waiting another minute before getting out means...
The Soviet comedy Ivan Vasilievich features a Time Portal version, connecting the inventor's apartment to Ivan the Terrible's throne room. However, given that the part about the time machine working is All Just a Dream, we can't be sure if it would have ever worked, although Shurik's intention is, at least, to build a Time Portal-like device.
Looper appears to have the Terminator-type time machine 30 years from the film's time, which The Mafia uses to cleanly dispose of those they want to kill (i.e. they send a message into the past, warning their predecessors about the time and the place, who then send a Looper there with a gun; the future mafia send the target with a bag over his head and payment for the hit in the form of gold bars; the Looper kills the target, incinerates the body, and gets paid).
A case of Fridge Brilliance with gold bars, by the way, as finding 30-year-old currency in large amounts would probably be more trouble than its worth. It would also attract the attention of the cops, considering time travel is illegal.
It's been suggested that the Time Portal must be the only feasible method out of the ones listed, by dint of the fact that all of the others would allow time travelers to have come back to visit us in the past/present, which would presumably be noticeable - more out-of-the-blue E.T. Gave Us Wi-Fi moments, for example. A Time Portal requiring a "receiver end" to be built before travelers can come back would mean time travel is only possible as far back as the invention of the time machine. On the other hand, it could just be an Extra-Strength Masquerade at work.
The mechanics of the trip back in Mark Twain's A Connecticut Yankee in King Arthur's Court are never explained, but time travel forward was due to the wizard Merlin, even though there was no magic in the book before this.
Time Dilation Fields are used extensively in Larry Niven's Known Space stories, most notably ARM and World of Ptavvs. The Slaver Stasis Field is a kind of Time Dilation Field: inside one, time stops. World of Ptavvs has a character who's been in one for a very long time (in the outside universe, of course; from his perspective he just now turned it on).
In Poul Anderson's series of short stories and novellas about the Time Patrol, the members of the Patrol use distinctly TARDIS-like vehicles, ranging from one- or two-person motorcycle-like "time scooters" to larger, multi-passenger time transports.
Near the end of The Forever War we find out some humans are using a spaceship as a time-dilation type of time-machine in order to get reunited with people separated by FTL travel.
The Time Matrix, from the Animorphs mythos, appears at first to be a basic TARDIS-type, though it's notable that it's (realistically) regarded consistently by the characters as the greatest weapon ever created. Then it gets really weird. For example, if mixed or vague coordinates are given, it will actually create new universes to fit the specifications.
Several of Robert Rankin's novels involve time travel, most often by means of a talking time-travelling Brussels sprout named Barry, who can share his powers with people if shoved in their ear. Largely, it seems implied that Barry is a Back to the Future type 'time machine' - although physical locations rarely seem to be a bother. Barry was also cited to be the driving force behind Wells' Time Machine, inhabiting a metal box in the back. Oh and he's Elvis Presley's best mate.
Time travel in Dan Bayn's Tempus setting is Terminator style. You can only travel to the past, and once you've arrived, you cannot go back — time is like a funnel in Tempus, with an infinity of possible futures spiralling into the present until just one becomes the past, and going forward in time would scatter you among those many futures like dust in a hurricane. Basically, it's an excuse to have cool futuristic tech in the modern day.
The M.I.N.D. Machine of Dinoverse is between a Terminator and Time Cop type device, which can also breach dimensions. When it comes to time, you Can't Take Anything With You, including your body, but you end up in a new one and have to get something done before it lets you come back. There is no such restriction with interdimensional travel, but it doesn't take you back.
The Time Machine gamebook series is all about traveling to the past with a time machine to unravel mysteries, then traveling back and forth between various eras once you're in the past. You never actually get to see what the time machine looks like, and your amount of control over where and when it deposits you varies heavily from page to page.
In the book Sonic the Hedgehog in the Fourth Dimension, Sonic the Hedgehog and tails use a Time Treadmill to race back to the beginning of time. Physics is slightly more realistically applied than usual, as both Sonic and Tails get exhausted and have to take turns running, and their previously indestructible shoes, made specifically to withstand the force of their running, get demolished.
While the TARDIS in Doctor Who in theory can go anywhere in four dimensions in practice, it breaks so often that it only really works if you don't care where you're going. It doesn't so much break down as take you where you need to go.
"Carnival of Monsters" and "The Five Doctors" had Timecop style Time Scoops, machines that could beam in objects from anywhere and anywhen to the machine's present, without needing any equipment at the other end.
The episode "The Girl In The Fireplace" revolves around Time Portals.
Also totally random in their targeting, and their reliability in the case of the titular fireplace.
The Daleks' time-travel technology has varied over the years. In "The Chase" and "The Daleks' Master Plan" they use TARDIS-like time vessels, but in "The Evil of the Daleks" and "Resurrection of the Daleks" they use portal-style "time corridor" technology. (According to fanon, their minds are too hidebound to be really comfortable with the job of navigating a time vessel.) But then in the 21st-century series, the Cult of Skaro, at least, have time-vessel capability built into their power armour.
The Star Trek: The Original Series episode "Return to Tomorrow" was the first episode in which the crew deliberately used a time-travel mechanism they'd stumbled across accidentally in an earlier episode. They flew at warp speed very close to a star, and by controlling the vector with which they pulled away they travelled to a specific time in the past.
And a unique sort of time travel in the Star Trek: Voyager two parter "Year of Hell": You couldn't actually go forward or back, but you could delete objects from time. This would negate all changes caused by that object (except that time travellers and other ships with "temporal shields" were not affected).
Seven Days has a Terminator-type that goes back, you guessed it, exactly seven days, except when it's eight days one time due to an upgrade.
Or seven years in one case due to another alien ship crashing, providing more fuel.
Or only a couple days due to an unexplained breakdown. Honestroy, the Sphere broke down more times than it worked right.
Phil of the Future has the Diffys' van as a time machine. It's always broken, though, for some reason or other.
Kamen Rider Den-O has time-traveling trains, which generally work in Back to the Future fashion. The biggest difference is that you can't travel freely: the trains require a ticket to a specific point in timenote created by "scanning" an individual with a blank ticket, which then registers the date of an extremely strong memory, and then can only go between that time and the "present". There's also an extremely rare Infinity Ticket that lets the bearer go whenever he wants, but the DenLiner's Owner has it and only lets the heroes use it in times of immense crisis.
Feng Shui uses the Time Portal method of going through time. Characters travel time by means of going through the Netherworld, a weird mystical realm made up of loamy grey tunnels as well as whatever stuff its inhabitants can Shape into being that acts as a Portal Network between different junctures in time. The main method of effecting changes in the timestream is by capturing or destroying Feng Shui sites, Places Of Power that generate Chi.
The first Ape Escape is built off of this: main antagonist Specter, a white monkey that got his hands on a helmet that supercharged his intelligence, uses a newly invented time machine to attempt to change history so that monkeys ruled the world, and main protagonist Kakeru (Spike in the dub) must use the same machine to go after him.
In Scribblenauts, you can summon a time machine that can take you to a few predetermined time periods. One of these led to a meme:
"I FUCKING TRAVELLED THROUGH TIME AND JUMPED ON A DINOSAUR AND USED IT TO KILL MOTHERFUCKING ROBOT ZOMBIES."
Chrono Trigger has an interesting mix of three types: the Epoch is Back To The Future-type, while the Timepod is a Terminator-type, and the gates are Time Portal-types.
The Journeyman Project uses a Timecop approach (which helps since that's what the player is), depositing the agent at points where time has gone all ass-over-teakettle... by comparing all of history to a flimsy CD containing all known history or something (lolwut?). Each trip has a time limit that seems surprisingly lenient, as long as the agent doesn't achieve catastrophic failure.
The sequel has a cooler time machine entirely self-contained within a metallic space suit (mobile TARDIS-type?). In addition to allowing instantaneous time travel, the suit has a cloaking mechanism, a temporal anachronism detector, and permits instantaneous translation of the written and spoken forms of all languages (except Latin written backwards). Notably, the suits worn by the live action actors in the game's cutscenes were designed by the same group responsible for the suits from the Turtles films.
The third game has a modified version of the spacesuit time machine, equipped with holo-projectors and voice synthesizers, allowing the wearer to imitate any person he scans. This is done so the player can actually interact with characters in the past (and get punched by Genghis Khan).
Tales of Phantasia has a combination of TARDIS- and Terminator style time machine in the sunken city of Thor. It can send the user anywhere in time and space but does not come with them. The game also features Time Travel by magic spell, but only two NPCs can use that spell.
The Master Sword in The Legend of Zelda: Ocarina of Time is a Time Portal that transports Link 7 years into the future when he picks it up (also aging his body in the process, so it shows traits of a Time Dilation Field as well), and 7 years back when he returns it to the Temple of Time.
The ocarina can also move objects in time, as is shown during the ending scene of Ocarina of Time, and exploited more fully in the sequel The Legend of Zelda: Majora's Mask, where it can take Link to the start of the three day cycle, setting up that game's "Groundhog Day" Loop.
In The Legend of Zelda Oracle of Ages, the Harp of Ages can at first only open Time Portals in fixed spots, is later upgraded twice: The first upgrade makes it Timecop-style, transporting Link to the past while opening a return portal; the second upgrade allows Link to freely between the game's two time periods; the present, and 400 years into the past.
In Achron, human and vecgir players can build chronoporters / slipgates (which act as Terminator-type projectors) while grekim units can all time travel without external assistance (making them living Back To The Future-types).
The Alpha and Beta suits from Time Shift. The beta suit has the interesting adaptation that damage to the 'jump' drive allows you to use time powers.
Actually its designed to work that way, the jump drive just lets you go back and forth much more greatly than the 10, 15 seconds you can in combat. It was designed for military purposes, presumably they would remove the jump feature so everyone couldn't screw with the timeline.
Dr. Richtofen from Nazi Zombies found that the Teleporter is capable of time travel through overcharging it with Element 115: first on accident, bringing them to an abandoned theatre in Berlin, 1962; then on purpose to present-day Siberia.
Serious Sam has a interesting take on the time machine, the Time-Lock The machine itself is a stationary object found in Eqypt, you can only travel backwards and only to another time the machine was 'armed'.
Persona 3 FES has multiple doors which open to different points in the main cast's history. Most of these doors only allow you to see what is happening and not interfere but the door in the lounge of the dorm travels to the mall where they can interact with what is happening. This door is eventually used to travel to the moment when the Silent Protagonist makes his Heroic Sacrifice.
Time travel is the theme of Steins;Gate and there are a couple different kinds. Or rather, there's one kind, but how well you can use them is fairly limited. SERN in the future has your classic go back in time kind of machine as does Amane Suzuha but the device normally seen in the present, the Microwave Phone, is only able to send small data packets. If you go over the threshold protected size in any time travel, errors appear, which for physical objects is turning into a mysterious green goo. Data merely gets corrupted and cut off after the size limit is reached. Naturally, this is hard to work with.
In Homestuck, Dave gets a pair of turntables that can accelerate or reverse the flow of time around him. He uses them to go back to the past to Set Right What Once Went Wrong. The turntables also have the distinction of being one of the very few forms of time manipulation in the series that doesn't outright create Stable Time Loops (thanks to the universe's built-in precautions against Temporal Paradoxes).
Breakpoint City has a few of these. We've seen two cars, a portal, and a brain swapper.
In Times Like This, the time machine in question is a handheld device cobbled together from a cell phone, two lasers and a piece of Sesquicentium. Once activated, temporary time portals (or "time windows") can be generated at will.
The various starship drives in Starslip are kind of incidentally time machines of the TARDIS type. There's also Deep Time's timesuits, which are also TARDIS-like, but in suit form.
SCP Foundation: SCP-1968 is a bronze torus of unknown origin. Officially it merely alters a person's memories so that they do not match current historical records. The truth, and what makes it qualify for Keter status, is that it's actually a time machine. The person's memories don't match history because of Ripple-Effect-Proof Memory. The Foundation is keeping the torus on hand as a last resort. They speculate that this might not be the first time someone used it to save the world either, but there's no way to confirm it.
Danny from Bravest Warriors built a time machine so he could kick the crap out of his childhood bullies and tell his past self to wear more flattering clothing. When his friends expressed concerns that doing so might cause a Time Paradox or worse, he dismissed them claiming that if anything went wrong his future self could go back in time to destroy the time machine. Immediately after he says this, Danny's future self appears and smashes the time machine to pieces with a bat. Wallow claims this happens every time someone builds a time machine.
The Simpsons: Homer travels back and forth between the dinosaur age and his own time in the Crime and Punishment segment in Treehouse of Horror V. His time travels have consequences on future events, though, which haven't been solved by the end of the episode.
Meet the Robinsons features a TARDIS-type time machine: It is essentially a jerry-rigged (flying) car like the DeLorean, and can be driven like a regular car, but has instantaneous space/time-travel capabilities as well.
The Kim Possible movie A Sitch in Time had an ancient Time Monkey Idol that created a Time Portal used by the villains, and unexplained Time Portal-opening watches for the heroes.
Gargoyles has a few episodes with a TARDIS-style amulet, the Phoenix Gate. The characters can't use it to change the past because they didn't. Time travel's funny that way.
The Adventures of Jimmy Neutron has one (in "The Tomorrow Boys"); the Chrono-Arch. This is a Terminator-like type of time-travel machine (Jimmy had to find it back when he went 15 years into the future, which he luckily did), and has an additional view-mode.
Additionally, in "The League of Villains", Jimmy built a wormhole generator: the Wormhole Generator 9000. The invention sent all of Retroville (except Jimmy, the gang and Tee) to the prehistoric past with no hope of ever returning, until Jimmy appears. This can't really count as a time-traveling-machine, though, since Jimmy had to disrupt the wormhole in order to get all of Retroville back to their time (leaving the bad guys in the past).
In another episode, Jimmy invented a small gizmo which could accelerate or reverse time. And he ended up in the past by it, so he had to use Bamboo Technology in order to get them back. Ultimately, someone uses the gizmo on all of Retroville, sending them back to the point where the adventure didn't even start! "Deja vu"!
In Xiaolin Showdown the ineffectual villain Jack Splicer had apparently built a working Terminator-style time machine years ago. It only goes backwards and there's no forward counterpart since he was never able to provide sufficient power to make it useful (he could only go back two seconds in time).
In Beast Wars any ship equipped with Transwarp Cells has Back to the Future style time travel. This includes ships that were never intended for Time Travel, like the Autobot Shuttle the Maximals use at the end of the series.
The whole Golden Disc plot involves the original Megatron leaving a message for his descendants, expecting transwarp drives to develop to the point where they can be used to travel to a specific point in time in order to alter the course of the Autobot-Decepticon war.
The ridiculous point is the episode where the Maximals start sending out transwarp probes to search all of time and space for Optimus Primal and his crew. The amazing thing is that they almost succeed, considering this is an impossible task, and the probes can't scan for shit (it passes right above the stranded Maximals and doesn't see them or the Axalon). There's also the question of why they'd go into all this effort to find them, given that they're not terribly important figures. Optimus Primal is not the leader of the Maximals unlike his ancestor.
Doc Greene finds one in Transformers Rescue Bots. It was built in 1939, and the only reason it remained unused for so long was because there was no power source capable of sustaining it until nuclear power was invented.
Mr. Peabody's WABAC (Wayback) Machine took him and Sherman to visit historical figures.
The Danger Mouse episode "The Hickory Dickory Dock Dilemma" had a grandfather clock that took the hero and his assistant Penfold through time, from prehistoric days to a future London. Contained a gratuitous Doctor Who reference.
Randy Cunningham: 9th Grade Ninja: McFist had Viceroy build one in "Randy Cunningham: 13th Century Ninja". To Viceroy's disappointment, instead of using it to destroy the Ninja, McFist wanted to use it to travel back to a time his favorite breakfast cereal still hasn't been discontinued.
Truth in Television / Portal to the Past - Okay fine, only sort of. But during the controversy over the Large Hadron Collider in the run-up to its activation, as media all over the world started blabbering about the end of the world due to some pretty poor evidence, some supporting scientists put out a reassuring theory. Apparently, after some calculations were done, it proved more likely that time travellers would come out of the first full power collision, than the LHC bringing about the end of the world. There's a chance someone in the future will make a machine that can target wormholes in the past and use them for time travel, if they know about them. Given that the LHC may be capable of generating wormholes with fraction-of-a-second long lifespans, this may give them a 'year zero', an earliest point for time travellers to come back to, as it would be the first instance of a wormhole forming close enough to Earth to be useful. The LHC has not made a full power collision yet.
Also in real life, Dr. Ronald Mallett has proposed a time machine that works more on lasers and particles than macroscopic objects, but otherwise is quite similar in manner of operation to the system from Primer, described above.
Except the key thing with the Alcubierre drive is that it avoids any time dilation effects because the ship is "stationary" within the bubble so the ship wouldn't actually travel back in time but could still arrive before a light pulse.
If you had a wormhole and used time dilation to make time pass faster on one end, you would eventually get a time portal.
A Krasnikov tube would be similar to this. It's built with the ends at different times. The entrence and exit time match the departure and arrival times of the space-craft making it. If you built one and went through it, you'd arive a little after you left. But if you spend ten years building one in a giant circle, then anyone from the future can follow you back.
A Tipler cylinder would technically be a Time Dilation Field that lets you go back. Specifically, it skews time and space so moving to one side takes you back in time a little. If you move in circles around it fast enough, you go back in time. Practically, it's Portal To The Past.
The current physics models predict that if faster-than-light travel is possible, time travel is also possible; that as far as we know neither is possible; but that if you could travel into the past, it would create a Stable Time Loop, and you wouldn't be able to change any history. A few models add that everything nearby would explode the moment you (or anything else) arrived in the past, or even at the moment the two ends of the wormholes approached near to each other within space.