What verse(s) would various sects/denominations/etc. of Christianity be interpreted as an instruction/a rule/a directive not to masturbate? What do other kinds of Christians interpret those verses as, if not that?

Why do you ask, Christian? ...

At any rate, the classic (if somewhat strained) example is Genesis 38:6-10 >>Judah got a wife for Er, his firstborn, and her name was Tamar. But Er, Judah's firstborn, was wicked in the LORD's sight; so the LORD put him to death. Then Judah said to Onan, "Lie with your brother's wife and fulfill your duty to her as a brother-in-law to produce offspring for your brother." But Onan knew that the offspring would not be his; so whenever he lay with his brother's widow, he spilled his semen on the ground to keep from producing offspring for his brother. What he did was wicked in the LORD's sight; so he put him to death also.<<

Many reading the last lines in isolation interpreted it to mean that spilling ones seed on the ground was what was denounced as evil, but the essence of Onan's sin is greed, sinful pride, infidelity, disobedience and deception: he didn't want to sire a child who would legally be Er's heir, carry his name, and take the firstborn's inheritance away from Onan and his house and (legal) descendants.

It also fits into a larger story that Judah had sinned in the first place in marrying a Canaanite, and thus all his descendants by her were ipso facto wicked, unclean, and cursed.

In other words, the classic proof text isn't much of proof text at all. (And I don't hear many preachers promoting Levirate Marriage these days either!)

That being said, people have drawn on various passages in the Epistles enjoining us to never be slaves to anything, least of all fleshly desires, and that you must be the master of your body and your appetites, and not the other way around.

The point that must be remembered is that there can be nothing sinful about the mere act, otherwise, everyone who gives a sperm sample at a fertility clinic is sinning.

But self-love is sin itself. Typical masturbatory fantasies are lies flattering false gods: lust, fornication, and yourself. It feeds and feeds on narcissism ... and frustrated narcissism even more. It is usually accompanied by sloth and dereliction of duty, and the appetite for more also encourages these vices. It encourages a neurosis: a false view of sex, love, masculinity, the body, and yourself. All of this can make it very difficult to connect with a real woman the way you're supposed to when you're supposed to. In short: don't become addicted, and if already addicted, fight the addiction like Hell.

On the lighter side, reminding you of Christian liberty: if it's just that there's no suitable or available woman to marry or ones situation doesn't give that option, and it's 3 in the morning and the guy still can't get to sleep because he's got a stiffy to beat the band, and it's been weeks since he's had any relief, I don't think there's anything Scriptural against it. He should just be careful to keep his thoughts wholesome - or perhaps best not to think of anything at all other than how it feels.

But don't forget: If a man does what he believes to be sinful, even though it is not a sin, it is a sin for him.

"Jesus wept."
You know, over the kitten that gets killed every time you masturbate. :o)