I'm pretty sure the winner would be the IRS's modernization program, which was to write new software to process tax returns. It began over 16 years ago and has consumed over $12 billion (just for the software development portion).
$4 billion was spent on the first attempt at writing this software before they gave up in 1997 with no usable product. That's a $4 billion "app" nobody ever used.
It's been a few years since I read about it so things may have changed, but last read was they spent another $8 billion in the 2000s trying again, this time outsourcing the development to consulting firms with thousands of developers. And around 2005/2006 had yet to produce a system the IRS could use, forcing them to continue processing tax returns with paper and antiquated systems.
The estimated payroll costs for Windows Vista are estimated to be 10B. Now consider the costs for every Windows version released since 1985, and include R&D/marketing expenses.
But that's an operating system, not an application. You've got to give credit to the IRS spending more on one application than Microsoft spent on their OS.
OSes are not particularly complicated. I could imagine that tax laws require a lot more code (and tests) than dragging some windows around and scheduling processes. (Neither are easy, of course.)
That "one application" was software+hardware tasked with managing millions of hand-written paper forms. The electronic version of tax filing was far cheaper, and launched successfully.
$4 billion was spent on the first attempt at writing this software before they gave up in 1997 with no usable product. That's a $4 billion "app" nobody ever used.
http://articles.baltimoresun.com/1997-01-31/news/1997031030_...
It's been a few years since I read about it so things may have changed, but last read was they spent another $8 billion in the 2000s trying again, this time outsourcing the development to consulting firms with thousands of developers. And around 2005/2006 had yet to produce a system the IRS could use, forcing them to continue processing tax returns with paper and antiquated systems.