During the height of the consulting boom, large management consultancies (McKinsey, Boston Consulting Group, Deloitte (soon to be Braxton), Ernst & Young, etc) sought out others with graduate degrees to help fill in the gaps, both for content knowledge, and just sheer smarts. You can look on any of their websites to find out a little bit more about what they do. It varied whether you were expected to stay in health care or do just general consulting. I am aware of them even coming to med. schools to put on recruiting shows and interview med students. Currently consulting is basically in the doldrums. Layoffs are common and most projects are overstaffed. Given what I know about MBA recruiting, I think the salad days of med students just wandering over to the McKinsey recruiter and saying, "Hi, I have an MD, I've never held down a steady job before, but can I have a job?" are basically over. The ones with big health care practices like Deloitte and BCG however may still be looking.
There are also boutique firms that specialize in health care issues. These span the spectrum, from the Hunter Group that focuses on turn-arounds (enacting huge layoffs usually), to Tiber that focuses on improving reimbursement and strategy issues.
Lifestyle is pretty brutal at the big firms. Usually 4 days/week on the road, 1 day/week in the office. Average workweek >90 hrs. Beginning pay packages average around 100k + relocation and perks.
Upside: varied assignments, lots of travel (if you like that sort of thing), lots of intellectual stimulation, experience can help you jump into business ventures (McKinsey is the training ground of many CEOs in the Fortune 500), money upside is good.
Downside: lots of travel, job security is not great (most firms practice an up or out career path), once you start you can't go back to clinical medicine very easily, much less autonomy than being a clinician in a private practice.
This is a very brief skeleton sketch. I hope it helps. If you have a specific question I can take a crack at it.
