Why do indebted governments fear deflation? It's widely accepted among people who follow finance that various governments around the world, including the US government, are doing (or their central banks are doing) everything possible to keep their economy out of a deflationary state. (cf. Ben Bernanke's "drop dollars from helicopters" comment.)  The rationale given is that deflation makes your debt more expensive and harder to service.

This rationale doesn't make sense, at least not on the surface.  With inflation, prices in general go up as the value of the currency goes down; with deflation, prices in general go down as the value of the currency goes up.  Therefore, in a deflationary environment, debt service would become more expensive but all the other things on your budget become cheaper, and therefore, as long as debt service comprises less than 50% of the budget, doesn't the country come out ahead?
They don't or shouldn't, fear deflation absolutely. But it's a complicated issue because there are two causes of deflation/inflation. One is changes in the money supply, the other is changes in production.

Changes in production that cause prices to fall are beneficial to everybody. Society becomes materially richer, and this is the great economic success of the last 100 years.

However, prices will also shrink if the money supply falls, since there is less money to buy things with. That in and of itself wouldn't be such a big problem in a market based environment where prices could adjust up and down. However the one thing that can't adjust its price is debt, debtors have made a commitment to  re-payments irrespective of whatever the money supply and deflationary situation is.

It depends where you are in the world right now, as to whether the money supply is expanding or contracting. The situation in Greece is particularly problematic:



This is very similar to the Great Depression pattern in the US which saw a 30% drop in the money supply 1929-1932. Once something like this gets established, it creates self-reinforcing negative feedback loops throughout the economy. For example, part of the reason for the drop is Greeks moving money to banks in other countries that they expect to stay in the Euro. But because of that, Greek banks can't make new loans without violating their regulatory requirements, and that further causes the money supply to shrink.