How bad does job hopping look if the hops are all increases in responsibility? These hops are between different organizations. The orgs I've been part of tend to be smaller in general, so advancement internally is really limited (someone has to retire or die). I have the following job history:
Entry Level Tech - 3 Years
Analyst - 4 Years
Programmer - 6 Months
Manager - 6 Months
IT Director (4 Directs, but much bigger scope) - 1.5 Years
Now there is an available position I've been asked to consider that is director level and much much bigger in scope which likely has a few directs who have directs.
Are the short lengths of stay going to catch up with me? Or is that more than mitigated by the increase in responsibility?

Job Hopping
I'm having the same issue, except i've been a contractor in order to take care of my responsibilities. Your job stints are probably fine, since the small companies limit mobility. You outgrow a position, you outgrow a position.
I've included a great blog that answers this exact question. Also, the article she wrote for US News:
http://money.usnews.com/money/blogs/outside-voices-careers/2013/02/06/are-you-a-job-hopper
http://www.askamanager.org/2013/02/are-you-a-job-hopper.html
"It is hard to fail, but it is worse never to have tried to succeed." - Theodore Roosevelt
"Public opinion is a weak tyrant to that of private thought." HD Thoreau Walden
Depends
If you're goal is senior management, you're may be on the fast track with that quick jump up to a director role. If you intend to leverage your network for opportunities in the future, short stays in roles may matter, but if you're dealing with folks that know you well and know why you made your career decisions, they're likely to be supportive. Even going in cold turkey to a new company will not necessarily be a bad thing with that sort of experience.
As a point of reference, here has been my trajectory:
Project Coordinator, Latin America Operations - Large Software Company - 1 year
Manager, Data Quality - Internet Startup - 1 year
Manager, Marketing - Mid size market research firm - 4 years
Senior Analyst, IT - Large Healthcare organization (similar to your company, to get promoted, someone basically has to retire or die) - 6 years
Senior Analyst, Internal Research - For-Profit Education company - 1.5 years
Manager, Pricing - Large Consumer Electronics firm - 3 months (current)
Point being, I've jumped around a lot into different roles in different industries and have a valid reason for each jump. Some recruiters will shy away, but that'll always be the case for one reason or another. My ultimate point, is don't worry too much. You're trajectory will likely be no crazier than the next person (e.g. ME!), and if you keep solid relationships with your network, few will care about your quick jumps from role to role.
If someone wants to give you more responsibilities and you're interested, take it! But remember, there is more to life than work. Consider introspection for each new role. One of Mark's stories about comparing a yellow M&M (representing work) held at arms length up next to the sun (representing home life) has always stuck with me. In other words, they may be the same size and look relative to your eye, but that sun is way, way, way more important than the M&M (sorry, Mark, if I botched the story a bit :)) Realize with every promotion and every increase in responsibility, how that affects your personal life and your professional goals. And be crystal clear on the reasons for every career move, you'll be asked in interviews. I know!
Cheers to you both, thank
Cheers to you both, thank you very much. I am interested in moving into senior management. I don't have the full details of the roll yet. I do try to maintain a careful work-life balance so that will be key in looking at this roll. I do try to trade money for time when I can. Mark related a story where they started getting him a car from the airport. In a similar bent, when I get a roll with increased salary and increased commitment, I make a point of trading some of that salary for convenience like having someone mow the yard, or have a house cleaner come in occasionally. That way the time spent with the family may be somewhat less, but more quality. That said, I have some confidence that this roll won't be one of those soul absorbing jobs. I don't think I've made it that high yet.
By the way, Calouden, you nailed it, I'm in healthcare. People get stuck in roles and never move, so there is a lot of shuffling between orgs for advancement, which is tricky because there are only so many hospitals in any given location.