As Jeremy Butterfield points out, "The relationship between the forms rack and wrack is complicated," and the spellings are sometimes interchangeable (Oxford A-Z of English Usage, 2013).

As a verb, rack means to torture or cause great suffering. The verb wrack means to wreck or cause the ruin of something.

The noun rack means a frame, an instrument of torture, or a state of intense anguish. The noun wrack means destruction or wreckage.

Idiomatically, we may rack the billiard balls, rack up points, and roast a rack of lamb. But when it comes to nerve-(w)racking experiences or (w)racking our brains, most writers, dictionaries, and usage guides admit to being (w)racked with uncertainty. See the usage notes below.

 

Examples:

• "To delight in seeing men stabbed, poisoned, racked, or impaled is certainly the sign of a cruel temper." (Joseph Addison)
• "Penny was wracked with sorrow for his friends. (Marjorie Kinnan Rawlings)
• "I have sometimes been wildly, despairingly, acutely miserable, racked with sorrow, but through it all I still know quite certainly that just to be alive is a grand thing." (Agatha Christie)
• "I'd like to be buried Indian-style, where they put you up on a high rack, above the ground." (Jack Handy)
• "The baby's cry is becoming nerve-wracking." (Paddy Chayefsky)
• "But having to be present for merchandise deliveries that Eunice ordered online or on the phone was nerve-racking." (Joseph Wambaugh)
• "Lud had been going to wrack and ruin for centuries." (Stephen King)

• "We're pleased you're going to do right by that house. It's been going to rack and ruin for years." (Doris Lessing)

Usage Notes:

• "Rack and wrack are confused so frequently that most dictionaries now list both spellings for the verb meaning torment and the noun meaning destruction."
  (Margery Fee and Janice McAlpine, Guide to Canadian English Usage, 2nd ed. Oxford University Press, 2007)
• "In some senses, the verbs rack and wrack are synonymous, and the two words, each as either noun or verb, are nearly interchangeable at some points. The usage problems arise over which spelling to use where there seems to be a possible or a clear overlap in meaning. Most Edited English will prefer rack your brain, wrack and ruin, storm-wracked, and pain-wracked, but other Standard written evidence, including some Edited English, will use the variant spelling for each."
  (Kenneth G. Wilson, The Columbia Guide to Standard American English. Columbia University Press, 1993)
• "The expression (w)rack and ruin preserves the original sense of destruction. (These days rack and ruin is the more common spelling in both British and American English, by the evidence of the BNC and CCAE.) . . .
  
  "As often, figurative uses of rack and wrack have enlarged their domains and made the spelling interchangeable wherever the sense of severe stress and destruction apply. Wrack seems to be gaining ground there, although still less common than rack in collocations such as nerve-racking and racking one's brains."
  (Pam Peters, The Cambridge Guide to English Usage. Cambridge University Press, 2004)
• "Wrack is commonly used as a verb synonymous with the figurative senses of rack . . ..
  
  "Probably the most sensible attitude would be to ignore the etymologies of rack and wrack (which, of course, is exactly what most people do) and regard them simply as spelling variants of one word. If you choose to toe the line drawn by the commentators, however, you will want to write nerve-racking, rack one's brains, storm-wracked, and for good measure wrack and ruin. Then you will have nothing to worry about being criticized for--except, of course, for using too many clichés."
  (Merriam-Webster's Dictionary of English Usage, Merriam-Webster, 1994)
• "The New York Times Manual of Style and Usage has a great idea here: Never use wrack, because it confuses people. Instead, when wrack means wreck, just use wreck. (But when you mean 'inflict damage,' spell it wreak. You 'wreak havoc on'; you never 'wreck havoc' because havoc is unwreckable.)
  
  "O.K., keynoters, let's rack 'em up: It's traditional to rack up your opponent with a good tongue-lashing for having led the country to wrack and ruin, and after you rack up a victory, you can wreak patronage vengeance from high atop your city on a hill."
  (William Safire, Quoth the Maven: More on Language from William Safire. Random House, 1993)
• "The noun wrack means ruin or destruction, and generally is confined to the phrase wrack and ruin and wracked with doubt (or pain). The verb wrack has substantially the same meaning as the verb rack, the latter being preferred."
  (The Associated Press Stylebook and Briefing on Media Law 2011. Associated Press, 2011)

Practice:

(a) He placed his trunk in the luggage _____ and took a seat by the window.

(b) The bridge had fallen into _____ and ruin.

Answers to Practice Exercises

Glossary of Usage: Index of Commonly Confused Words