I believe much of the research on this (certainly the better known stuff) is work done by Elizabeth Warren, the same one who is now a senator. You can find an example here:
http://www.law.harvard.edu/programs/petrie-flom/workshop/pdf/warren.pdf .
To quote that, "Out-of-pocket medical costs averaged $17,943 for all medically bankrupt families: $26,971 for uninsured patients, $17,749 for those with private insurance at the outset, $14,633 for those with Medicaid, $12,021 for those with Medicare, and $6545 for those with Veterans Affairs/military coverage. For patients who initially had private coverage but lost it, the family’s out-of-pocket expenses averaged $22,568.
Among common diagnoses, nonstroke neurologic illnesses such as multiple sclerosis were associated with the highest out-of-pocket expenditures (mean $34,167), followed by diabetes ($26,971), injuries ($25,096), stroke ($23,380), mental illnesses ($23,178), and heart disease ($21,955).
Hospital bills were the largest single out-of-pocket expense for 48.0% of patients, prescription drugs for 18.6%, doctors’ bills for 15.1%, and premiums for 4.1%. The remainder cited expenses such as medical equipment and nursing homes. While hospital costs loomed largest for all diagnostic groups, for about one third of patients with pulmonary, cardiac, or psychiatric illnesses, prescription drugs were the largest expense."
Though not included in the above quotes, the article also makes the point that serious illness is also often associated with lost income.
I broke my shoulder a few years back, and with "good" health insurance paid about $4.5K out of pocket over the next 6 months. Some of that was bad luck -- I was out of town when the break occurred, and started in a hospital where initially they were going to do the surgery (admitted me, etc.) but then decided they weren't the right place to do it and I was released, went home, connected with a local surgeon, etc. But none of my drug copays (which were minor) or PT copays ($45 per, 2 visits per week for a LONG time and well worth it) counted toward my out-of-pocket max. And while I was fortunate to have plenty of paid time off work available, unsurprisingly, breaking the arm while on vacation with my family led to necessary itinerary changes and associated costs. Plus, I couldn't drive for easily 3 months, maybe more (and I certainly couldn't bike for a much longer time than that).