Conveniently Coherent Thoughts

""The mind is not a book, to be opened at will and examined at leisure. Thoughts are not etched on the inside of skulls, to be perused by any invader. The mind is a complex and many-layered thing.""

- Professor Snape, Harry Potter

People do not always not think in complete sentences, and often idly think about trivial things. 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, but likely not in a way that contributes to the plot.

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.

Film
"Controller #1: They're screwed. Controller #2: They're dead. Johnny: Did I leave the iron on?"
 * Played for laughs in Airplane! II. 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.


 * Played with somewhat in the second X Men film, 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.

Live Action TV

 * 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." It gets worse.
 * Generally the case on Heroes with Matt Parkman's telepathy.
 * 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-sequiters 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.

Literature

 * The novel The Trouble With Jenny's 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 and deconstructed 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.

Videogames

 * When you read people's minds in Destroy All Humans! they give you a succinct sentence. Maybe not a relevant one, but what did you expect?
 * Mind-reading in Golden Sun functions much the same as speech, typically providing a clarification or amusing aside to whatever an NPC says when addressed.