Well, since everyone's adding their own experiences to this, I'll share my own as well.

I used a simple trolley-style car jack to remove a bunch of broken-off cedar fence posts. I screwed a large eye bolt (or is it called an eye screw?) into the top, attached a chain wrapped around the jack's business end, and started lifting. Of course I wasn't able to get right over top of it, but there was enough leverage with the handle to make it work. After I ran out of stroke, it was loose enough that I could just use a long 4x4 as Stig described.
It's things like this that make you smile when you're done and haven't broken a sweat.
The great thing about this, as opposed to digging it out, is that I still had nice compacted earth all around and it didn't take much to install new (slightly smaller) posts in the same holes. I just packed some sand and gravel around the outside with a large steel bar. Ok, there may have been a little bit of sweat with that part...