The core characters of the 1970's/1980's sitcom Taxi include:
Alex Reiger (Judd Hirsch)
The heart and soul of the series. After having a nice office job, his lack of ambition got him fired, he lost contact with his family, and ended up a taxi driver content to spend the rest of his life driving cabs. Potrayed by Judd Hirsch.
Ambiguously Jewish: Not too gently confirmed in a late episode by two members of a co-op board.
Berserk Button: He doesn't react well when he gets compared with pelicans.
Beware the Nice Ones: In "Bobby's Big Break", when Louie was ranting about how he was going to put Bobby through ultimate hell when he returned to the garage, Alex finally snapped and tore the front of Louie's wire-mesh dispatcher's cage with his bare hands and proceeded to yank Louie out of the cage and grab him roughly by the scruff of his shirt until Louie compromised.
Boyfriend Bluff: In "Elaine's Old Friend", Alex posed as Elaine's college professor boyfriend, Bill Board, an act that managed to woo Elaine and even Elaine's friend while she was on a date with her own boyfriend. Even afterward, Elaine considered they should take their relationship further, but the end of the episode left it ambiguous as to whether or not anything was going to come out of it.
Only Sane Man: And how. When your friends and co-workers include an egotistical actor, a wacky immigrant mechanic, a burned-out relic of the '60s, a boxer one straw short of a haystack, and a vile toad of a dispatcher who likes to torture his employees, you know you must be the most normal one of the bunch.
Token Good Teammate: Despite Alex's initial sour demeanor when given one of his friends' problems, he always comes through in the end and everybody knows they can rely on him. Secretly, however, it's something that Alex resents, as learned in "Mr. Personalities", when Latka (as Alex) relates all of Alex's innermost thoughts to a psychiatrist.
The Unfavourite: The reason Alex is strangely nonchalant about his father having a heart attack.
Break the Cutie: He always comes closer than anyone to getting out of the garage, and always has his dreams crushed in the most humiliating way possible. Louie delights in reminding Bobby what a failure he is.
Butt Monkey: Bobby has the unfortunate plug of being Louie's favorite of the cabbies to pick on.
The Bus Came Back: For a guest appearance in the episode "Bobby Doesn't Live Here Anymore."
Real Life Writes the Plot: Jeff Conaway was fired after his heroin addiction became too disruptive to the filming schedule. When he was finally completely unable to film an episode, Bobby's lines were split between other characters where they fit just as well, causing the producers to realize they didn't need the character at all.
Berserk Button: There's one word Louie hates more than anything... "accident".
Big Ego, Hidden Depths: In "Louie Goes Too Far", Elaine asks Louie if his privacy has been ever violated (this after she caught him peeping while changing clothes). We then learn that Louie has to go to the kids' department of the store each time he buys new clothes, feeling very humiliated.
Big Little Man: Louie spends most of his time in the dispacher's cage during the pilot, and the audience has a big laugh when they see Louie at full height.
The Friend Nobody Likes: No one, except Jim and perhaps Latka. The "friend" part is questionable, but he does start to hang out with the cabbies outside of the garage more and more as the series progresses.
Jerkass Façade: Very strongly implied. Notably, in "Louie's Fling", Louie starts crying so that Alex can help him. When Alex does, Louie teasingly announces that he only pretended to cry so that Alex would come through, pissing Alex off, but when Louie realizes Alex is serious, he quietly laments that his tears were real.
Jerk with a Heart of Gold: Louie had his moments. Once, the cabbies suspected that he would tell Latka was marrying a call girl to get his "green card". But when the inmigration agents asked him, he told them Latka was actually marrying for love.
Stalker Shrine: Somehow the cabbies think that Louie's pasting of a photo of Zena's face over a bikini-clad calendar girl seems to be quite weird (That's how Jim knew of Zena in "Louie Meets The Folks").
"Reverend" Jim "Iggy" Ignatowski (Christopher Lloyd, seasons 2-5)
A gentle burn-out hippie, Christopher Lloyd's character first appeared in a one-shot role in the first season, being hired to officiate Latka's green card "wedding", but he was so well-received that the producers brought him back early in Season 2, becoming a regular just a few weeks in.
Ambiguous Disorder: Jim often confuses reality with fiction (he once referred that his father taught him to be a man along with his brothers Hoss and Little Joe), he once got obsessed with being the one who watched E.T. the Extra-Terrestrial more than anyone else in New York City, forgets important stuff frequently and considers Louie his best friend.
Can't Get Away with Nuthin' : A single marijuana-laced brownie sent the bright, wealthy, and promising young James Caldwell into a downward spiral of drugs in the '60s and transformed him into the Jim Ignatowski that the cabbies all know and love.
Cloud Cuckoo Lander: Jim lives in a world of his own, from having visions of the original Mouseketeers to mistaking a cigarette machine for a record machine, to having a funeral for a dead horse that doesn't exist.
Genius Ditz / Idiot Savant: Jim may be slow at times (justified since he used to be a drug addict), but you'll be surprised at how much his apparent social delusions prove to be quite accurate, especially in "Jim Joins the Network."
The Sunshine Cab Company's mechanic. An immigrant from an unnamed (perhaps Eastern European) country who firmly believes in the American Dream (Type 1), he is innocent and polite but extremely naive and can have a hard time reconciling the ways of "the old country" with his new life. Created as an Expy of performer Andy Kaufman's stage persona of "Foreign Man" and intended as a Breakout Character, the show eventually took him in a Denser and Wackier direction via a multiple personality disorder. But The Power of Love for fellow old-worlder Simka Dahblitz brought him around, and Latka became the second and last regular character (and longest-serving one) to get married in the course of the series.
Aborted Declaration of Love: Latka tried to tell his feelings for Simka, but he turned into Vic Ferrari before he could complete his speech.
Absentee Actor: Andy Kaufman was extremely reluctant to do a sitcom and made it a requirement in his contract that he wouldn't have to appear in every episode. He doesn't; in fact, Latka appears in fewer and fewer episodes as the series progresses.
Actor Allusion: There were a number of in-joke references to Kaufman's stand-up act, including having Vic sing the "Mighty Mouse" theme.
As Long as It Sounds Foreign: Latka's native language. Most of this was Kaufman's creation and he had to teach it to Carol Kane when she made her first appearance as Simka, but a few specific words were added by the writers ("nik-nik" = "love", for instance).
Berserk Button: Go ahead, try to mention Vic Ferrari to Latka. Or mess with his woman, Simka.
Beware the Nice Ones: It has been shown that despite his innocent demeanor on the job, Latka can at times get carried away in his thoughts, such as in the episode "Fantasy Borough", where he daydreamed that he and Louie switched roles, with Latka as the top sarge and Louie as the harrowed mechanic. Ultimately, it climaxes with Latka about to execute Louie by firing squad. When Louie snapped Latka out of it moments later and pissed him off again, Latka simply said "fire."
Cursed with Awesome: The Vic Ferrari personality helped Latka score with multiple women, but the reason he wanted to dispose of Vic was because Vic continuously interfered with Latka's own life and even attempted to take over completely.
A Day in the Limelight: Subverted, as Latka was still a central character, but episodes that stood out for being primarily focused on him: "Paper Marriage", "Mama Gravas", "The Apartment", "Latka's Revolting", "Guess Who's Coming For Brefnish", "Latka's Cookies", "Latka the Playboy", "Mr. Personalities", "Simka Returns", and the remainder of the series' episodes that involved his relationship with Simka.
Did You Just Have Sex?: Simka realizes that Latka "did it with another woman" immediately after he walks into the door in the snowstorm episode.
Reality Subtext: Andy Kaufman's character develops multiple identities? You don't say!
Ruritania: This is the only explanation given on the show from where Latka might be from. We've seen drawings of the country like nothing that can be identified as a known location as well as some of the dress styles that suggest an Eastern European land.
Played by Carol Kane, she is Latka's feisty Distaff Counterpart. Initially appearing as a one-off character in Season 2's "Guess Who's Coming to Brefnish", her relationship with him fell apart owing to his prejudice against the "mountain people" of their home country, as she happened to be one of them. After an unsuccessful attempt to make a go of it in Omaha, Nebraska, she returned to New York City in Season 4 and ultimately gave Latka a reason to give up his multiple personalities. By season's end they were wed, and she was a regular in the fifth and final season.
All Periods Are PMS: In "Simka's Monthlies", the final episode to air, this threatens her marriage to Latka because she cannot make the meeting with the immigration board that would finalize her U.S. citizenship (thus risking deportation).
And This Is for...: Simka slaps Latka for each family member of hers he unknowingly mocked with his jokes in "Guess Who's Coming for Brefnish" ("I hope you have a small family...").
Single Woman Seeks Good Man: In her re-encounter with Latka, Simka tells she was "used and thrown away like and old shoe" when referring to the relationships she had after the events of "Guess Who's Coming For Brefnish."
Women Are Wiser: As previously mentioned, Simka would often stand up to Louie for Latka.
John Burns (Randall Carver, season 1)
A somewhat nerdy college student from the Midwest who became a cabbie after having to go to the garage since Alex didn't have enough change for fifty bucks. He had a couple of episodes centered on him (with one of them focused on his Accidental Marriage), but he was quickly Demoted to Extra and was written out after the first season. Portrayed by Randall Carver.
Accidental Proposal / Accidental Marriage: In "The Great Line", he picks up a girl at Mario's with the line, "Let's just skip everything and get married." To his surprise, she accepts the proposal and they get married...and presumably stay married for the rest of his time on the show.
Insane Troll Logic: Once Tony complained that the apples in the snack machine were "old and mushy". Here's John's explanation:
"They do put new apples in the machine, but to get to the new apples, you have to eat all the old apples, but because the old apples are so old, very few people eat them. So, by the time you get to the new apples, they're old apples".
Ascended Extra: While he never quite made "regular" status, Jeff had the episode "Crime and Punishment" centered on him when Louie accuses him of stealing car parts. Plus, Thomas filled in for Andy Kaufman during rehearsals whenever Kaufman was not present, and his role in the episodes where he was given something to do basically took the "Louie foil" slot that Latka often held.