Did Goku Really Say “Power Comes in Response to a Need, Not a Desire”?

Yes. Goku says "power comes in response to a need, not a desire" to Gohan in the Hyperbolic Time Chamber, during the Cell arc of Dragon Ball Z, and the words are the English dub's. It is one of the few Dragon Ball lines that gym accounts share which the show actually contains.

The verdict

True. ComicBook.com's list of the series' best lines places it in episode 156, "Bow to the Prince," with the context: Goku and Gohan are a year inside the chamber, Gohan cannot reach Super Saiyan by effort, and Goku explains that the transformation answered a need in him, the death of Krillin on Namek, rather than a wish. Wikiquote's Dragon Ball Z page is thin on dialogue and does not carry the line, so it rests on the editorial tier, as most of this site's Dragon Ball entries do; the wording is stable across every copy, and the scene is a well-known one.

The sentence the poster drops

In the scene the line has a second half: the need has to be created. Goku is not offering Gohan a consolation for failing, he is telling him that the way to transform is to manufacture the desperation, and the rest of the training sequence is Goku trying to frighten his son into it. That is a stranger and more Dragon Ball idea than the poster version, which reads as a maxim about strength coming from adversity. The show's version is closer to an instruction manual for a specific transformation, and the payoff is not in the chamber at all: Gohan finds the need when Cell crushes Android 16's head in front of him, which is the series saying that Goku was right about the mechanism and wrong to think it could be rehearsed.

Why it survives when the other Goku lines do not

Dragon Ball's motivational canon online is mostly fabricated, because the real Goku talks about food and fighting and rarely about anything a poster can use; the gym slogan this database already caught in Vegeta's mouth was invented to fill exactly that gap. This line is the exception, a genuine sentence of Goku philosophy, and it survives because it is also good advice about the show: every Saiyan transformation in Z arrives on grief or rage and never on wanting. Goku's verified lines on this site include the Frieza speech that exists only in the dub, which is worth reading next to this one, since both are the English writers giving Goku more eloquence than the Japanese did, and both are real as English.

How we checked

The verification process asks for a primary or editorial source, and an editorial one supplies the episode and the scene. The entry in the fact-check database is true, with the note about the missing second sentence, and the rest of the series is on the Dragon Ball Z hub.