As some who lives abroad with no plans to return home any time soon ...
I'm not sure I could live ANYWHERE permanently. Not close to home, not far from home. I'm just a wanderer at heart, and with the internet / skype / etc ... the parts of American culture (I watched every game of the NCAA Tournament, every NFL game I wanted too, etc - all in HD ... I talk to my family regularly via video chat, etc) that I really want to have I don't have to miss. This isn't 1860 anymore.
Short of places like North Korea, Cuba, or Vietnam, I don't know of any country that requires you to renounce citizenship.
I doubt anyone would do it, save the most Lee Harvey types amongst us. I believe I've read that you cannot renounce your American citizenship solely for the reason of avoiding taxes. Some have tried this though it seems to work best if your name is GE, Exxon, or Dart.
Lots do. For instance, off the top of my head, I know that Norway and Singapore do.
We lived 3 years in Burma (without TV) and I loved it.
Like 94, we are very seriously looking at moving to the Caribbean and setting up shop.
I would move to Australia tomorrow and never look back.
Would never give up my citizenship however.
I lived in Japan for almost 2 years and enjoyed the experience, but I wouldn't live there again since it was so expensive. If I did relocate permanently abroad it would have to be a place where I can make a decent salary (think: US standard of living) and live inexpensively (like Central/South America). Someplace in Europe would be doable for me culturally, but economically they are having a lot of problems. The US is having problems too, but there's a lot to be said about living near your family when times are tough, which is why it makes sense to stay put.
I'd live in Kazakhstan, booming economy, lots of potential for growth, cheap as hell, hot babes.
I always thought I wanted to live for a long term abroad. Well, I've been living abroad (w. europe) for two years now with at least one more to go. I've really liked it, but I'm starting to get a bit homesick now.
It sucks when everyone in the USA gets together for Homecoming or some Memorial Day trip and you can NEVER go because it is hard to spend $2k (and jetlag) on the total trip just to spend 3-4 days with your family or friends. Also, I have missed almost two full years of sports because I just can't stay up at 2am to watch a football game live. It sucks. Sunday afternoons are totally different over here. (Plus, no one cares about college basketball, or any type of american football....i.e., you watch games alone)
Also, you miss weddings, air conditioning, bbq, free wifi in public places, mexican food, and if you don't learn the language quickly, you miss out on a lot of stuff socially.