People do not always think in complete sentences, and often idly muse on trivial things for a few seconds before passing to the next thought. However, when telepaths read minds, they don't have to sift through all of that 'mental' garbage. The thoughts that they read are usually incredibly coherent (and relevant to the plot).
This might be an Acceptable Break from Reality; forcing the audience to hear a bunch of garbled thoughts might be entertaining note to the author, but likely not in a way that contributes to the plot. Could also be considered a kind of Translation Convention — just as you can understand a guy speaking French if the character understands it, you can understand the garbled contents of someone's head if they're filtered through the mind of a trained telepath.
Anime and Manga
Averted in Mahou Sensei Negima! with Nodoka: When she reads minds with her artifact she has to ask what she wants to know to cause them to think about it.
Averted in Kotoura-san. Haruka eventually realized even with her telepathy she didn't get to pick up everything, like her mom's remorse for disowning her.
Zig-zagged in A Certain Magical Index. After Accelerator's fight with Kihara Amata, he was left without use of his electrode and could barely think coherently on his own. However, when he's approached by telepathic Espers, he regains enough of his calculation ability to have a mental conversation with them. The only reason he's able to think coherently in the first place is because of the telepathic Epsers giving him some of their calculating power.
Played for laughs in Airplane II: The Sequel. After the Mayflower space shuttle malfunctions, someone in the space traffic control room asks "What do your people think?" The audience is briefly granted the power of Telepathy so we can hear the controllers' thoughts.
Controller #1: They're screwed. Controller #2: They're dead. Johnny: Did I leave the iron on?
Played with somewhat in X2: X-Men United, when Jean Grey starts to lose control of her psychic abilities. Apparently she can usually tune out the garbage and focus on the particular thoughts she's looking for, but when her powers start to malfunction, she hears every thought of every person in the very crowded museum she's in. This gives her a headache, which causes her to involuntarily short out all the TV screens around her.
The novel The Trouble With Jennys Ear features an especially blatant example: the title character is asked to testify at the trial of a sleazy salesman, using her telepathic powers to determine whether he had committed intentional fraud in selling a local fisherman a useless "fish whistle." She listens in, and comes up with the ambiguous phrase, "You can always catch a sucker if you fish deep enough," which he naturally claims is an endorsement of his product rather than a comment on the gullibility of his customer.
Averted in the Discworld book Small Gods - Om can't read minds because they're too chaotic, but he can get a feel for the general shape of them.
Discworld has another example when mentioning Granny Weatherwax's skill at Borrowing: birds and small animals have small, pointed minds tightly focused on feeding, mating, fighting, building nests, avoiding predators, seeking prey. Humans have a diffuse cloud of abstract thoughts and notions.
Averted in C.M. Kornbluth's The Mindworm. When the telepathic title character picks up thoughts, they're almost always the standard "stream of consciousness" type.
Averted in the The Skinjacker Trilogy. When 'skinjacking' a human, random disjointed thoughts just bounce around.
Averted in Harry Potter with Legilimency, which likewise reveals thoughts in a disjointed manner and requires great training in order to sort out which thoughts are important.
Averted in "The Mind Field" (a story that appeared in The Magazine of Fantasy and Science Fiction within the last few years—I forget the author's name). A machine is invented that lets the French government read the minds of visitors to the French White House-equivalent. The machine reveals images they think of, not words and sentences, though the images are important clues—e.g., where bodies are buried.
In the Firebird Trilogy, telepathic mind access provides coherent information to the accesser. This is somewhat justified, as the telepaths don't merely read the thoughts off the surface off the mind; they are actively directing what they see.
In The Twilight Zone episode "A Penny For Your Thoughts," the protagonist gains the ability to read minds, and hears a disgruntled bank employee planning to rob the bank. After he denounces him, though, it turns out that the man's been idly thinking about robbing the bank for years, but he'd never actually go through with it.
True Blood is a pretty straight example. There are occasionally a few stray thoughts that don't give Sookie exactly what she's looking for, but they still almost always fall into line with what we expect the character to think ("this jerk better leave right now" "Doesn't she look like a tasty little meal" etc..) and never anything random like "did I water my plants?" or "what a cute skirt, I could use one like that."
Happens to varying degrees in No Ordinary Family where the daughter is a mind-reader. Usually the person will think a clear sentence related to what she's trying to find out, but sometimes it'll just be random nonsense.
Averted on Buffy the Vampire Slayer: The first thing the temporarily-psychic Buffy reads from a boy in her school is "Man, one day these pants are gonna fall right off my ass."
Generally the case on Heroes with Matt Parkman's telepathy, to the extent that Noah Bennett is able to foil him by thinking in Japanese.
It might have been subverted in the Bad Future episode "Five Years Gone" — an older, more experienced Matt Parkman has no trouble reading the mind of a confused Hiro Nakamura, who at that point only spoke Japanese. It's possible that Matt learned to understand Japanese in the five years, or that his powers developed to such an extent that they overcame the mental, linguistic barrier.
Played with in the Firefly episode "Objects In Space." When River is shown reading the minds of the rest of the crew, their thoughts come in the form of clear sentences. However, in most cases they are non-sequiturs or irrelevant to the current situation or conversation. Except for the thoughts River gets when Zoe and Wash are making out; those actually come in the form of crashing ocean waves and other sensations that cause River to sway and stumble.
Somewhat subverted in the Doctor Who serial The Time Monster. When making telepathic contact with Jo Grant, at first she hears a cacophony of voices. But the Doctor gets her to concentrate on the "main" one and we get a clear conversation about how to save the day.
Used with Kelly's mind-reading power on Misfits, to the point where she can even understand a dog's thoughts in perfect English.
Mind-reading in Live A Live gives out fully constructed sentences.
In Ghost Trick, ghosts don't have voices and communicate directly through thought. The once-dead whose deaths have been averted via Time Travel can also communicate this way, and hear the thoughts of ghosts. This trope is usually played straight (justifiably for the ghosts; not so much for the living), with a few exceptions:
1) Although most thought takes place in English, the in-conversation "flashbacks" are implied (and all but outright stated) to be visual thought transferred in the same way as the rest of the conversation. The other member in the conversation sometimes comments on things they could not have possibly known if they didn't get to see the flashback. Even then, they're incredibly well-organized.
2) At one point, Sissel has to keep a secret from Kamila, and kind of fails utterly by thinking about the secret he's trying to keep.
Early in the game, Ray interrupts Sissel's Internal Monologue and finishes it for him. It's still incredibly coherent, but there is no barrier between any form of thought and anyone else, making this an odd combination of Conveniently Coherent Thoughts and Power Incontinence that is played with in a way that can't quite be defined.
Ray manages to keep quite a few secrets for quite a long time, including his appearance (he appears as a desk lamp for the entire game), because he has been a ghost for over ten years, and has a lot of experience. This even extends to (MASSIVE SPOILERS) outright lies; he convinces Sissel that he is the man in red, and tells him that he will cease to exist by morning.
Freeman's Mind and a bunch of its spinoffs have characters who thoughts are consistently coherent. Most people think with pictures or develop feeling and occasionally think with actual words when they are in deep thought, but the main character ALWAYS thinks in full sentences that are easily understandable.
Teenagers from Outer Space has a novel way of handling this; when a PC tries to use telepathy, the GM makes up three different things the target might be thinking, and the player rolls a die to determine what they pick up. Thus, you may be trying to find out if your cute classmate fancies you, only to stumble upon her plans for world conquest through absolute control of toilet paper supplies. This is entirely appropriate for the game.