I've been researching our options for health (medical) insurance while we're in Florence. Our "American" policy covers us for the first 180 days after our move, so we have to change over pretty soon. There are basically two roads we can take...
Our first option as non-EU immigrants is to join the Italian Public Health system ("Servizio Sanitario Nationale" or SSN). To be eligible all we need is our Permesso di Soggiorno and official Residency. Although the fee varies according to family income, I believe coverage for our family would be under 500 Euros for the year - a bargain when you look at U.S. health insurance prices. Under this plan, everything - from doctor's visits to prescriptions to surgery - is free (in some cases there's a small co-pay for specialists or certain procedures). There seems to be a consensus that this is good (but no-frills) coverage. The doctors are well-trained and the facilities are up-to date. The down sides might be that the primary care doctors don't accept appointments (so you have to just wait in line during office hours), and the hospitals tend to look a little worn around the edges. In general, SSN sounds like a great option if you're living in Italy. These are the sites I found most helpful about Italian healthcare: Agenzia Sanitaria di Firenze, and Expattalk (my favorite forum with tons of info about living in Italy and lots of answers to insurance questions).
Option number two is purchasing International Health Insurance. The web is full of companies offering medical insurance to "expat" individuals and families - but there are so many variables that it's really hard to navigate through them all. The few companies/plans that I bookmarked and thought might work for us are:
Inter Global - plan descriptions and rates all right on the website.
Bupa International - trusted UK company, lots of info on the web, but there was a glitch on their "Get Quote" page and I could never get a final price without calling them.
International Medical Group - website explains benefits, premiums, etc. fairly completely, and you can request a quote online.
International Citizens - Another one that looks pretty good.
Specialty Risk International - Their Worldwide Health Insurance seems to have a reasonable price for coverage that includes treatment in the U.S.
Most of these policies offer the choice of whether or not you want coverage in the U.S. - but it's much less expensive to elect coverage only in Europe or your foreign country of residence. They also require that you live outside the U.S. at the start of the policy, and don't reside in the U.S. for 6 consecutive months inside the policy year. Most are long-term, annually renewable plans (unlike some "travel" insurances which you have to reapply for).
If we were staying in Italy permanently I would definitely go the route of the Italian SSN, but we've decided we still want to keep our options open in the U.S. - so we're in the process of applying for International Health Insurance. Instead of going directly to one of the providers listed above, I've found an insurance broker who we'll be going through: Global Insurance Net. Global is a company out of Florida that represents about 12 companies with international health plans. They've already been really helpful with sorting through the details and finding the best policy for our needs. Carlos, the president, has responded personally and promptly to every email I have sent him, and he's found us a plan that is within our budget and covers all our needs. I only wish I had found them earlier when I was trying to make sense of all this on my own!