In the season six finale of The Big Bang Theory, Raj FINALLY overcomes his selective mutism and is able to talk to the girls without alcohol. Penny, Bernadette, and Amy find themselves just wanting him to shut up while he goes on an on about his (lack of a) love life.
From his very first conversation in the "Pilot", Abed in Community is shown to have a habit of unloading a bit too much information unless someone stops him.
On The Cosby Show, Vanessa's friend Cara is a master at this, leaving pretty much everyone she talks to utterly dumbfounded. Cliff referred to her as "Turbo Tongue", and responded to every outburst she made with the same non-comprehending, "Thank you." Rudy's friend Kenny even snarks at her about this when she offers to fix him lunch:
Spencer Reid of Criminal Minds is this. He repeatedly goes off into rambles on subjects such as the relative lack of factual inaccuracies in Star Trek, the written differences between two serial killers and, perhaps most memorably, a thirteen minute non-stop off-the-top-of-his-head profile of a serial killer in order to stop the guy from killing him and Hotch.
CSI: Ronnie Lake, Sara's partner when she transferred to swing shift, had a habit of asking non-stop questions.
Having taken some "energy pills", Morwena in Doc Martin develops a bad case of this. The energy pills turned out to be methamphetamine.
David Tennant's incarnation of the Doctor (the Tenth) has a tendency to speak at a blurring pace when thinking or just generally excited which, combined with an equally prominent tendency for Expospeak and Technobabble, makes his speech nearly impenetrable to those without a pause button and/or a script; or are auditory-first.
This little moment from "42" is a great example. Just try to see if he takes a breath during any of it.
"Any number that reduces to one when you take the sum of the square of its digits and continue iterating it until it yields 1 is a happy number, any number that doesn't, isn't. A happy prime is both happy and prime. Now type it in!"
Amy has her moments, especially during the first "Meanwhile in the TARDIS" short, where, somewhat in shock from seeing the TARDIS interior, starts rattling off several questions, ranging from "What is a Police Box, did police come in boxes?" to "The bow tie, is it a cry for help?"
Game of Thrones: Nothing too bad, as he always makes sense, but Tyrion does earn a reputation for never shutting up. He's physically incapable of remaining silent for too long and almost always feels the need to break silences and strike up a conversation.
Corporal Ray Person of Generation Kill, due to an addiction to legal stimulants.
The whole cast of Gilmore Girls, especially Lorelai and Rory. The show's scripts were apparently twice the size of your standard television script due to this characteristic. Jared Padalecki once joked that the main requirement to work on that show was the ability to speak very fast.
Rachel in Glee whenever she is feeling outraged about something. Taken up to ElevenFifteen in Vitamin D when she was hooked on Sudafed.
[rattled out in under 20 seconds, while hyper-ventilating] Thank you so much, it really is a pleasure. While the Boys chose a selection of songs that cast an eye inwards on the irresponsible life choices and sexual hunger of today's modern teens, we have chosen a selection of songs that speaks to the nation as a whole during these troubling times filled with economic uncertainty and unbridled socially - because if there is two things America needs right now, it is sunshine and optimism. Also angels... (Okay.)
Emma Pillsbury, of all people, manages to pull off a flawless rendition of the impossibly fast patter from (Not) Getting Married.
On Hawaii Five-0 Dr. Max Bergman is prone to do this when something, usually work, sets him off. Masi Oka has proven on the gag reel that he is capable of improvising whole speeches for Max if he has or wants to.
In the episode "Spoiler Alert", the entire gang is greatly annoyed by Ted's extremely talkative Girl of the Week. Ted himself didn't realize this until they point it out to him. Hilariously, the episode ends with a Flash Forward three years later of her being engaged to a deaf guy.
Though not normally prone to this trope, Barney sums up the entire romantic history of a seven season show in 52 seconds:
Seven years ago when Marshall and Lily got engaged Ted saw Robin across a crowded room and I said "oh yeah you just know she likes it dirty," but Ted really liked her so we played "Haaave You me Ted?" They went to dinner, he walked her home, should have kissed her, didn't, lame. So he stole the Smurf penis, went back to her place, should have kissed her, didn't, lame. He threw three parties, they kissed on the roof but decided to be friends, lame. Then Ted wanted to take Robin to a wedding, she couldn't go, he went alone and met Victoria. Didn't kiss her either, lame. Not a great closer Ted. Then he finally kissed her, they started dating, she went to Germany. Ted kissed Robin, lost Victoria, Ted did a rain dance, got Robin. Ted and Robin broke up, Robin moved to Brazil came back with a Latin stud. Ted got jealous, got a tramp stamp, not really relevant to the story I just like mentioning it as much as possible. I hooked up with Robin, Ted and I stopped being friends, Ted got hit by a bus we made up...Robin and I started dating and I got fat her hair fell out. We broke up, Robin dated Don, I dated Nora. I cheated on her with Robin, I dumped Nora. Robin dated Kevin but not for long and then I met you and you took my Grandpa's watch, but I fell in love with you anyway and you let me fart in front of you and I asked you to marry me and you said yes so we came over here to meet little Marvin and that's everything. Also, I went on the Price Is Right and I won a dune buggy.
Carly from iCarly tends to do this, especially when she's feeling hammy. The best example would be her long rant about why she kissed bad boy Griffin in "iDate a Bad Boy".
Hawkeye from M*A*S*H had a tendency to do this once in a while. Particularly in the last episode.
Merlin from the BBC's Merlin is very prone to this, so much so that one of Arthur's earliest signature phrases is "Shut up, Merlin".
Invoked in the pilot episode of New Tricks when Sandra confronts a Dirty Cop by reciting one of his witness statements in motormouth fashion in order to fit it into the time he claimed to have spent getting it. Turns out he'd fit over forty minutes worth of words into less than twenty minutes of time.
Kelly from The Office (US) is well known at Dunder-Mifflin for being one. When she's plotting revenge on Jim and Dwight, Pam figures out she's up to something because she says hello to Jim without talking his ears off for 15 minutes. There is also a hilarious scene where the office has a gambling pool going involving Kelly explaining Netflix to Ryan in a single breath for over two minutes.
London on Open Heart. She says she speaks out loud to sort out her thoughts when she's thinking too hard.
Our Miss Brooks: Walter Denton does this when nervous, or when trying to polish the apple. In the episode "Cafeteria Strike", he reads off a student's petition in this manner:
Walter Denton: Whereas and to wit— Miss Brooks: That's pretty strong language, isn't it? A little on the pink side. Harriet Conklin: Listen, Miss Brooks. Walter Denton: When in the course of student's events, it becomes necessary to turn one's back on one's stomach, we the undersigned, exercising our constitutional right to peaceably assemble, and to form a committee to seek the redress of grievances, do hereby announce our firm intention of the Madison High School Cafeteria only to use the tables, chairs, water, napkins, and toothpicks provided therein. Until such a time that the duly appointed party or parties, namely Mr. Osgood Conklin, principal, or the Board of Education, responsible for the operational bog-down that has befallen this installation, do take such action that will improve the food, lower the prices and better the service in said cafeteria. It is also recommended the person, or persons, in whom this authority is vested, immediately see that the present chef in charge of preparing the food, and without any further frippery or fanfare, chuck him the heck off the premises. Well, Miss Brooks, what do you think of it? Miss Brooks: How much do you want for the picture rights?
Pushing Daisies: Ned is prone to babbling like this whenever he's nervous. And he is nervous a lot.
Ned: I was bored and snooping really just bored and trying to entertain myself so it was more really ipso facto snooping like when you go into the bathroom and read all the magazines and go through the medicine cabinet and I found this!
Generally everybody speaks rapidly, including guest stars, and conversational replies and rejoinders have little if any gaps in-between speakers.
Elliot in Scrubs occasionally communicates at "the speed of light", as J.D. puts it, mostly when she is angry about something. It's played for laughs, and other females are capable of understanding her, if not being able to talk just as fast.
Sarah Chalke has said in interviews that speaking incomprehensibly rapidly was one of the first of the character's traits listed on the audition script.
On Selfie Eliza tends to talk quicker than normal, on average, but just enough to be noticeable. When she really ramps it up, it's like there are no spaces between her words.
Eliza: Yeah, I'm gonna try to bump into some celebrities maybe hit a gifting suite, kick it with guerreche, yadhop, bingedrink till I'm white girl wasted... Henry: That sounds... Eliza: Hop by this pop-up party, get my grind on, swing by In-N-Out, kiss a hamburger full-make up, no filter, David Guetta.
David Hewlett is known for how fast he can belt out pages and pages of dialogue, especially as Rodney in Stargate Atlantis.
Michael Shanks as Daniel Jackson does the same thing in Stargate SG-1. As a result, the writers predicted the Atlantis season 5 two-parter with Michael Shanks as a guest star would have a much longer script than usual since Jackson and McKay would spend a lot of scenes together spouting Technobabble. According to the commentaries, they were right.
And then there's the time McKay gets high on Wraith enzyme.
Picard: "He just kept talking in one long incredibly unbroken sentence moving from topic to topic so that no one had a chance to interrupt ... it was really quite hypnotic."
Data was also known to drone on, especially in earlier episodes, until Picard interrupted with "Thank you, Mr. Data." In the ST:TNG pinball game, if you gutter a ball without scoring during a Bonus Round, and you hear Data's voice, press both flipper buttons simultaneously, and you'll hear Picard's "Thank you, Mr. Data" and get an additional 10,000,000 points. Picard occasionally used this to his advantage, getting Data to chat up people he didn't want to deal with.