My favorite exploding offer story is probably this one:
"I received the offer via voicemail while I was in flight to my second interview. The judge actually left three messages. First, to make the offer. Second, to tell me that I should respond soon. Third, to rescind the offer.
It was a 35 minute flight." −2005 applicant for federal judicial clerkships (p448 of "The New Market for Federal Judicial Law Clerks" )
Exploding offers can have a malign effect on market performance. Here's a just-published experimental investigation that focuses on how exploding offers contribute to the unraveling of a market:
Niederle, Muriel, and Alvin E. Roth, “Market Culture: How Rules Governing Exploding Offers Affect Market Performance," American Economic Journal: Microeconomics, 1, 2, August 2009, 199-219.
(In case you were always wondering how lawyers and gastroenterologists are similar, and different, these two papers will give you some clues, at least for when they are looking for jobs...)
Here's the Abstract of the AEJ Micro paper: Many markets encounter difficulty maintaining a thick marketplace because they experience transactions made at dispersed times. To address such problems, many markets try to establish norms concerning when offers can be made, accepted and rejected. Examining such markets suggests it is difficult to establish a thick market at an efficient time if firms can make exploding offers, and workers cannot renege on early commitments. Laboratory experiments allow us to isolate the effects of exploding offers and binding acceptances. In a simple experiment, we find inefficient early contracting when firms can make exploding offers and applicants’ acceptances are binding.