Name 3-5 well-known modern-day successful corporate moguls who
rebounded from spectacular failures to get to where they are today.

For example, Donald Trump, bankrupt or almost bankrupt with debts of
$x and is now worth $y today. you may use Donald Trump as one of your
examples.

Also, while I do not consider dropping out of college a spectacular
failure (ie. Bill Gates), I will accept flunking out of college as a
spectacular failure.

Richard Branson of Virgin.

Do UK moguls count?

Not quite what you're looking for but it looks like an interesting
bibliography of Blunders and Failures.

http://www.kipnotes.com/BlundersFailures.htm

Michael Milken
(See The Economist article "Michael Milken, comeback king" 25-Mar-1999)

Donald Trump

Henry Blodget (his post-blowup success can be debated, but he does
have a job as a journalist)

Shawn Fanning (his original idea failed... he now acts as a consultant)

Steve Jobs (left Apple once most people believed it had peaked...
returned recently, now look at the company)

Kaleil Tuzman (the movie Startup.com chronicled his failed dot com
venture... he now runs a successful Entrepreneurship workshop)

Ron Popeil (debatable if this guy's a true business mogul, but he's
made/lost/re-made millions in a cut-throat business)

Well there is Jeffrey Archer - a bit of a YoYo = not totally corporate

And /two/ Philip Greens

|Everyone knows the story of PG 1. He made a spectacular comeback from
the ruins of Amber Day and now owns a large chunk of the high street.|

http://business.timesonline.co.uk/article/0,,8210-1511147,00.html

I am pretty sure Robert Maxwell screwed up big time 
- before recovering with Pergammon and the Mirror

Jim Slater fell, but sort of resurrected himself as a City guru.
- now that was Slater-Walker and Spydar (sp?)

Nick Leeson seems to be doing alright - in a low key sort of way.

Philip Greens is on the money, thanks frde-ga.