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.

The verdict

True. ComicBook.com's list of the series' best lines places it in episode 156, "Bow to the Prince," with the context: Gohan has been trying hard to get stronger and nothing is working, and ComicBook.com adds that Goku himself unlocked Super Saiyan after Krillin died. Wikiquote's Dragon Ball Z season pages do not carry the line, so it rests on the editorial tier.

Finding the episode

The episode number depends on the list. Episode 156 is its place in the Japanese broadcast, where it is titled "On Your Knees, Cell! I Am Super Vegeta!!" and first aired on Fuji Television on September 9, 1992. "Bow to the Prince" is the title Funimation's English dub gave it, and the dub's initial run numbered it 141; it first aired in English on October 26, 2000, during that dub's Cartoon Network run. Wikipedia's summary of the episode opens on Vegeta's fight with Cell, before it turns to Gohan's training.

What happens after the line

The line is advice about one transformation rather than a maxim about adversity. In the episode where ComicBook.com places it, Gohan is training with Goku in the Time Chamber in an attempt to become a Super Saiyan. Four episodes later, still in the chamber, he asks Goku to give it everything he has; Goku transforms, fires a Kamehameha at him, and Gohan becomes a Super Saiyan.

Why it holds up

Unlike the slogan this database already caught in Vegeta's mouth, which has no scene behind it, this line is a genuine sentence of Goku philosophy, and it is also good advice about the show: Goku first became a Super Saiyan after Krillin died. Goku's Frieza speech, which is real in the English dub, is worth reading next to this one, and his sourced lines are on his quote page.

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, and the rest of the series is on the Dragon Ball Z hub.