Andromeda did several episodes exploring Alternate Universes in various ways: as a Near-Death Experience, and as a result of one character's ability to view potential futures. The most noteworthy was "The Unconquerable Man", which was an entire Clip Show playing out events from the show's history with a different lead character.
Illyria mentions being able to live seven different lives at once in different universes back in her days, including a universe made entirely of shrimp. She tired of that one quickly.
Awake is about a detective experiencing parallel realities after a car accident, one in which his wife has died, one in which his son has died. He uses tenuous cross-universe clues to solve crimes. The validity of the realities and the possibility that one is a subconscious response to trauma is always in question. The series ends with the possible introduction of a third reality in which both wife and son are alive.
These eventually became a running gag on the show, with Anya often mentioning universes she could potentially send people to: the universe of infinite Wednesdays, the universe without shrimp, the universe of nothing but shrimp...
At first, "Superstar" appears to take place in an alternate reality where Jonathan is the eponymous character, but it later turns out that he had cast a spell that altered reality itself.
There's also the universe as it was Before Dawn and Post-Dawn.
The Community episode "Remedial Chaos Theory" features the group rolling a die to choose who will go to the door to get the pizza. Abed warns that this will create 6 (actually 7) alternate universes. Everyone else of course dismisses this, but we the audience get to watch each one unfold. The differences ranges from different characters hooking up, mental break downs occurring, everyone having an awesome night, and everything going to shit. The versions of the characters in the universe where everything went to shit end up being recurring villains.
"Inferno" has an alternate totalitarian Britain (branching off at least around the "defence of the republic act, 1943"), which is in a still greater rush to get free power from tapping the magma of the Earth. It is destroyed, with the Doctor able to just avert the similar events happening a few hours later in his "home" alternate. Not bad at all.
"Turn Left": Donna Noble has an entire alternate universe built around her, where she never met the Doctor, and he consequently dies after the events of "The Runaway Bride". It does not fare well. In fact, the universe without the Doctor is pretty much a terrible place to be.
"It Takes You Away": The Solitract, a sentient parallel universe that was exiled from the main universe, and has become the stuff of Time Lord bedtime stories.
The second season of The Flash (2014) introduces Earth 2, an alternate world with many of the characters having duplicates. It's stated that there are an infinite number of universes, but this is the only one that appears to have a direct line to Earth 1 via the breaches that have resulted from the paradox singularity that opened in the season 1 finale. When traveling between the universes, characters experience glimpses of other alternate worlds (read: shows). The overall technology level of Earth 2 is higher than that of Earth 1, partly thanks to the S.T.A.R. Labs particle accelerator working successfully (as far as the public is concerned), although much of the tech has a Zeerust feel. Additionally, Atlantis is a real place there. The Flash of that world is not Barry Allen (who is just a CSI on Earth 2) but Jay Garrick (his nickname is Crimson Comet instead of Scarlet Speedster). There is also Gorilla City in a tropical rainforest, a refuge for intelligent gorillas. Meanwhile, Oliver Queen never made it off Lian Yu, his role as Starling City's protector having been taken up by his father, known as the Hood.
Earth 3 is mentioned in season 2 finale, which is the world where the real Jay Garrick (Henry Allen's double) is from.
The Alternate Universe on Fringe is a world where pockets of time and space become unstable due to Walter's kidnapping of Peter by crossing to the other side. In the AU, there are many details that differ from the characters' home universe, such as Martin Luther King Jr. being on the American $20 bill and the World Trade Centers still standing and Walter never went insane (and never hard parts of his brain removed), and is now the Secretary of Defense and head of their Fringe team, which takes far more drastic action to combat the far more drastic "Fringe Events" that occur "over there". Also, they're keen to show the presence of zeppelins, just so you know it's an alternate universe.
Game of Thrones Ascent, which follows the plot and events of the TV show (such as the death of Rakharo or Xaro Xhoan Daxos' betrayal) but incorporates elements of the novels: like Vaes Tolorro or Catelyn taking two Freys as wards.
One of the Christmas Specials features a world in which Artie never got on a wheelchair. As a result, there's no glee club, and Mr. Schue is an alcoholic and still married to his manipulative wife Terri. Also, Rachel never went to New York to work on Broadway and remained in Lima working as a librarian, Puck and Finn never graduated and remained being Jerk Jocks, Kurt didn't graduate either because, without the support and help of the glee club, he was bullied twice as much, and Quinn, without Artie's help and support, never could recover from the psychological trauma of being stuck on a wheelchair after her car crash and committed suicide.
There's also the episode in which Tina is knocked unconscious and she wakes up in a world where she has traded places with Rachel, that is, Tina is the club's main lead and singer while Rachel has to stay in the back and never gets a solo.
Grimm: There's at least one alternate universe where the Wesen run free and probably from their come from. In this universe Wesen can not vogue and humans live like in the Dark Ages.
Hounded: When Rufus Hound is presenting a new show, he always gets pulled into a parallel universe by his Future Self.
Kamen Rider Dragon Knight uses the concept of alternate universes, accessible through mirrors. The Earth Kamen Riders are chosen because they are genetic doubles of the original Kamen Riders from the alternate universe of Ventara.
Kamen Rider Build is the first series not to use the Shared Universe established by the end of Decade, mainly because the backstory (Japan being split in three by mysterious walls that erupted from the Earth in 2007) is incompatible with the other shows, though they cross into the mainline universe in the movie Kamen Rider Heisei Generations Final Build And Ex Aid With Legend Riders. In the final arc of the main series, the protagonists enact a plan to merge their Earth with another universe's — implied to be the main universe — in order to stop the nigh-invincible Big Bad, which has the side-effect of retconning the events of Build out of existence.
Sci-fi series Lexx made this its staple. The first season of the show involved the characters jumping through an inter-universe rift twice, and in the second season once at the beginning, before the entire Light Zone was wiped out in the second Season Finale, forcing the Lexx (and a large amount of particle matter from the zone) to get forced back out into the other universe.
The season 1 finale of The Librarians 2014 has Flynn and Eve travel through three alternate realities, after Dulaque messes with the Loom of Fate. In each of the three realities, one of the Librarians-in-Training is the Librarian, since Flynn never took the job offer 10 years ago. Strangely, Eve appears to have been recruited as the Guardian at the same time, but has since been killed under the same circumstances (stabbed by Excalibur during the events of the pilot). Each of the three realities is a Crapsack World. At the end of the episode, all three help Flynn and Eve restore the Loom, even though this would mean that they themselves would be written out of existence. Their prime counterparts don't remember a thing.
Stone!Librarian world: Stone failed to prevent the full return of magic to the world and is running around the world, containing the worst of the magical problems, while countries are being engulfed in conflicts. This version of Eve used to be Stone's lover.
Ezekiel!Librarian world: Ezekiel's attempt to handle the House of Refuge crisis has Gone Horribly Wrong, and the world is undergoing a Ghost Apocalypse, as Team Ezekiel (he found a way to make money as the Librarian) struggles to find a solution. This version of Eve was Ezekiel's mother figure.
Cassandra!Librarian world: Magic is everywhere. Cassandra herself is a powerful wizard, having used magic to get rid of her brain tumor, which affected her personality. The world is coming to an end, and she plans to escape reality in a manner similar to Morgan le Fay with a small group of followers. This version of Eve was Cassandra's friend, although she disapproved of the use of magic. After Eve's death, Lamia became the new Guardian.
In "Tempus, Anyone?", Tempus kidnapped Lois and H. G. Wells and transported them to a parallel universe. In this universe, Lois disappeared while covering a gunrunning story in the Congo in 1993 and is presumed dead, Jimmy is "a whiz kid of the computer world" who has just bought the Daily Planet and Perry is running for Mayor against Tempus. The most significant difference, however, is that there is no Superman. In the parallel universe, Jonathan and Martha were killed in a car accident when Clark was ten (which he witnessed but was not fast enough to prevent) and he was bounced around foster homes for the remainder of his childhood. He eventually started a relationship with Lana Lang - this being Lana's only Lois & Clark appearance - who convinced him to keep his powers a secret and scolds him whenever he clandestinely uses them to help anyone in a minor way. At the time of Lois' arrival, he and Lana are engaged. This version of Clark never met the Lois of his universe as she disappeared before his arrival in Metropolis. Speaking of Metropolis, it is a dirtier, more violent city due to Superman's absence and almost everyone carries guns, typically semi-automatics.
In "Lois and Clarks", after Clark is stranded in a time window by Tempus, H. G. Wells brings the Clark from the parallel universe to the main universe so that he can be fill in for Superman in the absence of the normal version of Clark. This proves difficult for everyone, at least initially. Lois finds it very hard being around him as "it's like having Clark but not." For his part, the alternate Clark, who has a pretty lonely life, is attracted to Lois and the two of them have a "weird chemistry" that he doesn't really understand. Considering that Jonathan and Martha's counterparts in the parallel universe were killed in a car accident when their son was ten, meeting the very much alive normal versions of them is a particularly strange and painful experience for the alternate Clark.
Season 6 of Lost features an alternate universe where 815 never crashed, and many other details are different. Word of God has it that neither timeline should be called "alternate" or "parallel" as those words imply that one is more real than the other. Flash-sideways has been decided to be the proper term. People in the flash-sideways actually retain memories from the other timeline, with Desmond seemingly able to switch between both willingly. The finale blows the flash-sideways out of the water entirely.
The fourth episode has Curtis go back in time to the night he and his girlfriend Sam were busted for drug possession (the reason why he was on community service with the gang). After various failed attempts, Curtis does prevent the bust and him and Sam escape from the police, however it resulted on an Alternate Universe in which he was never on community service, which results in Kelly, Simon and Alisha being murdered by the probation worker, something Curtis had prevented from happening in the pilot.
Episode 2.6: A world in which a man who can manipulate lactose reveals their powers to the world, but later when more people with much more impressive abilities he is regarded as a joke in comparison, resulting on him going psycho and murdering Alisha, Nikki, Kelly and Nathan.
And then there's also that episode of Series 3 in which an old man gains Curtis' ability to travel in time and goes back to Nazi Germany to kill Adolf Hitler. However, he fails, Hitler obtains his phone and uses it to make gigantic technological advances that resulted in the Nazis winning WWII.
Homaged in Mystery Science Theater 3000, "Last of the Wild Horses", where Dr. Forester and TV's Frank get to quip at the movie, and evil Mike and Bots watch on from Deep 13.
"In Another Life", a man named Mason Stark is about to commit suicide, when he suddenly finds himself transported to another reality, pulled there by his more successful double (usually referred to as Stark), who has invented a device called the quantum mirror. Stark explains that he was using the mirror to meet his doubles from multiple universes in order to find out what his life could have been like. Then one of the doubles (known as Mace) murdered his wife and went on a killing spree. Stark has determined that Mason and Mace are from nearly identical universes, with the only difference being that Mason chose to try to shoot himself, while Mace opened fire on his coworkers. After finding himself in this universe, the insane Mace is trying to "put things right" by killing those, whom he shot in his own reality. In the end, the psychotic Mace and the cold-blooded Stark end up transported to other universes: Mace ends up in Mason's moments before the gun goes off, while Stark ends up facing off cops with a still-smoking gun (this ends predictably). Mason gets a happy ending, inheriting Stark's fortune and getting a second chance with the double of his deceased wife.
In "Worlds Within", the physicist Dr. Anya Kenway is recruited by the Burkmeer Research Facility to conduct experiments on a test subject named Sasha Vadimsky but commonly referred to as URS-28. He was born in Belarus in 1987. His mother was a technician at Chernobyl who was critically injured in the disaster and ended up in a coma. She did not even realize that she was pregnant. The severely mutated Sasha was delivered via Cesarean section and was not expected to survive. He was brought to Burkmeer at some point after the Soviet Union collapsed. The scientists at Burkmeer discovered that Sasha's body was producing tachyons, the previously only hypothetical particle that travels faster than the speed of light. They incorrectly believe that he does not have a mind. Anya, who is dying of multiple sclerosis and has only a year to live, is able to make telepathic contact with him and she learns that Sasha is connected to his counterpart from a parallel universe. His mother tells Anya that Sasha's mind is trapped in her universe and the experiments to which he is going to be subjected will kill him. With the assistance of her co-worker and former fiancé Dr. David LaSalle, she bombards Sasha with protons in order to create a tear in the space-time continuum. As a result, his mind is reunited with his body in the other universe.
Discussed in "Abduction". Jason, a science fiction fan, theorizes that he, Cody Phillips, Ray, Brianna and Danielle may have entered a parallel universe.
After Power Rangers was Un-Cancelled following the release of Power Rangers Samurai the previous series, Power Rangers RPM was revealed to take place in an alternate timeline to justify how the franchise could continue forward (since that series was set in a post apocalyptic timeline where the remainder of humanity were stuck in a single city).
Power Rangers Dino Charge is revealed in the following season to take place in its own separate timeline similar to RPM likely to justify the Mind Screw finale wherein the Rangers go back in time to kill Sledge and his crew 65 million years earlier and inadvartantly save the dinosaurs from going extinct thus resulting in a present day timeline where they live side-by-side with humans.
"Ace" Rimmer (what a guy!) on Red Dwarf came from an Alternate Universe, and travelled between dimensions. The Red Dwarf crew themselves had previously travelled into an Alternate Universe in the episode "Parallel Universe". Some episodes have featured similar alternate versions of characters and events, but were a result of time travel rather than passing into another Universe (notably "Timeslides" and "Inquisitor").
Rimmer enters a mirror universe in "Only The Good...", where he's captain of the ship, Kochnski is a Dumb Blonde, and The Cat a genius professor.
The dream world from "Back To Earth" is treated like this after the crew wakes up, and they find it hilarious that the people in it think they're real and the Red Dwarf crew are the fictional ones...
The books delve into this too. While multiple universes are established in Better Than Life, they really come into play in Last Human and Backwards. Last Human occurs when the crew return from Backwards Earth to the wrong universe and try to track down Lister's other self. In Backwards, Ace Rimmer is given a backstory behind Project: Wildfire and turns up to save the crew. Bonus points for the fact that both books, having each been written by Grant and Naylor separately, take place in alternate universes to each other.
In Seinfeld episode #137 "The Bizarro Jerry", Elaine is in a similar social circle where the Kramer equivalent is neat, George's is responsible, etc.
In the Shadowhunters episode "This World Inverted", Clary visits an alternate dimension where the Shadowhunters haven't needed to exist for centuries.
An interesting subversion: Clark wakes up in a mental asylum; apparently, he started having delusions of superdom in high school, and his "saving" of Lex in the first episode actually cost Lex his legs. Oh, and Chloe is a freaking nutcase. Of course, it was all a delusion caused by an escaped Phantom that attacked him in his barn and invaded his mind. John Jones (the Martian Manhunter) helped him escape by entering the illusion (as another inmate), and capturing the creature in a Kryptonian crystal.
Season 10 had an Alternate Universe as a major plot line: Clark discovers a kryptonian artifact called a "mirror box" and when activated it takes him to a world where the Kents never adopted him, but instead was raised by Lionel Luthor and goes by the name "Clark Luthor". Clark Luthor himself is brought to Clark Kent's world and causes no end of trouble before the original Clark manages to switch them back. Then it turns out the alternate Lionel managed to come through to the main world with Clark, taking the place of the original Lionel (who was dead) with a story that he'd faked his death. Then Clark Luthor uses his mirror box to come back and send our Clark to his world, where he helps the alternate Jonathan reconnect with Martha, and convinces Clark Luthor to try and use his powers for good, rather than live in Lionel's shadow.
Much of the Australian-Polish TV series Spellbinder takes place in a parallel world, which, initially appears to be primitive but is later revealed to be taking place After the End (an unknown Spellbinder experiment resulted in a global disaster). Temporary rifts occasionally open between our world and the world of the Spellbinders. The sequel Spellbinder: The Land of the Dragon Lord involves a machine, built by a Chinese inventor from yet another reality, that allows him to travel to any parallel world. The inventor and his companion from our world end up visiting several more worlds, including a world where much of humanity has been wiped out by a plague, and the cure that saved a tiny fraction of people also made them immortal and unable to reproduce, and another After the End world, where remnants of humanity try to rebuild after a devastating Robot War. The titular Land of the Dragon Lord is an alternate China, where ancient aesthetics mix with advanced light-based technology.
Stargate SG-1 has had many different alternate universes. Oftentimes, the "alternate" Samantha Carter is not in the military and is engaged/married to the "alternate" Jack O'Neill. Alternately Daniel Jackson was never part of the Stargate Program. More often or not, when this is used, Earth is under imminent Goa'uld attack.
In "McKay and Mrs. Miller", alternate Rodney is a really nice guy with lots of friends and alternate Sheppard is a member of Mensa, greatly annoying everyone with his egoism. In our universe, Rodney is the egoist one, Sheppard is a nice guy who took a Mensa test but turned down the offer to join.
In "The Daedalus Variations", a dimension-travelling Daedalus starship from an alternate universe pops up, and the team is trapped onboard when the ship continues to jump through alternate universes randomly. These include one where the planet Atlantis is located on hadn't formed into a stable planet, and one where they're attacked by an unknown group of hostile aliens. They can't shut down the dimension jump but they can reverse its direction, allowing them to get back before the engines quit on them and stranding them permanently.
And another is shown in the penultimate episode "Vegas". There, Sheppard is a homicide detective with massive gambling debts. He couldn't be included in the team because the stunt he pulled off in Afghanistan got him dishonorably discharged instead of getting Reassigned to Antarctica in time for the pilot. Rodney is more likable (though one scene suggests that he's simply better at keeping a lid on his ego) and the Wraith already made an attempt at culling Earth just to be repelled by the control chair in Area 51. Oh, and Todd got so delirious from starvation he's speaking in rhymes.
An Alternate Universe seems to be seen in the episode "What Is And What Should Never Be", but it's really all in Dean's head and everything is his perception — Mary's perfect, Sam and Dean are a bit wussy and the family is like any other. In his fantasy, his mother Mary and Sam's girlfriend Jessica were never killed by Azazel, so the Winchester family live perfectly normal lives and his Dad died peacefully. As Dean is utterly unhappy there, it seems he wants a extremely codependent relationship with Sam and the wracking memories of his family.
A real Alternate Universe, or rather a series of them, pops up in the episode "Mystery Spot" thanks to a repeating time loop in which Dean keeps dying. The iteration before the final time loop lasts months instead of the standard day, resulting in a dark, isolated Sam.
Later in the episode "It's a Terrible Life", where Dean is a Marketing Director for a firm and Sam is a techie in the same building with no memory of their hunter life beforehand apart from a few dreams, it's revealed that this was all a ruse from an angel to show Dean hunting is in his blood and he will always find a way to be a hunter. This is also a play on the It's a Wonderful Plot trope.
The second AU episode took place in the sixth season, where the brothers are sent to a universe note which is basically our world with a bit of hyperbole where Supernatural is just a TV show filmed in Canada, in which Sam and Dean are played by Jared Padalecki and Jensen Ackles, and there is no magic, demons, angels, monsters, or any supernatural beings at all.
And then there's "My Heart Will Go On", in which the Titanic never sank, somehow causing the Winchesters to own a Mustang, Bobby and Ellen to be married, and Celine Dion to be a lounge singer in Quebec.
The birth of Lucifer's son by a human woman causes the fabric of the universe to tear, creating a portal to an alternate universe known as "Apocalypse World". It's an After the End dimension where the forces of heaven and hell are locked in eternal combat and human civilization has been reduced to ashes.
In The Twilight Zone episode "The Parallel (1963)" an astronaut orbits the Earth a few times then lands in a world that is almost identical to the one he left but has subtle differences, he's a colonel instead of just a major, the president isn't Kennedy, etc. Then he wakes up in a hospital bed and it starts to look like it was All Just a Dream, before NASA receives a radio transmission from his counterpart.
Almost all of the Heisei Ultra Series (that is those from the 1990s onwards) take place in universes separate from the default Showa universe. This tends to result in things like monsters having different origins and the backstories of the Ultras being changed.
VR 5's Missing Episode, "Parallel Lives" had Duncan wake up one morning to find himself in a universe where Sydney, rather than her sister, had died in a car crash years earlier (of course, it eventually turned out that neither sister had actually died; both the car crash and the parallel universe were complex VR hoaxes. The episode was intended to test the viability of replacing the central character for the second season, a possibility which became moot when the series was not renewed).
Wizards of Waverly Place had an episode where Alex goes through a mirror and enters a parallel universe where nearly everything is about her and in her favor.
Xena: Warrior Princess, Hercules: The Legendary Journeys use a mostly standard Mirror Universe: Good characters become Evil, shaven characters become bearded etc. But regular Iolaus is a good, shaven, competent warrior and regular Joxer is good, shaven and incompetent; in the Mirror-verse, they are both good and shaven, but Iolaus is incompetent and Joxer is competent. There are some weird rules for the two universes. If a person (or a god) dies in one universe, he also dies in the other. Unless they happen to be not in their universe at the moment. This happened to the alternate Iolaus who was trapped in an "in-between" world when "our" Iolaus took a knife in the gut. Also happened to Hercules, as his double the Sovereign was killed while in this "in-between" world.