The best European country to live in? Tough question! There are so many, and each and every European country has something different to offer, something that may classify it as 'best', depending on who is looking.
As a seasoned traveller of the European continent and her islands (I am an American by birth and a global citizen by trade), here is a short list of some of the 'best' European countries...
The best European country to live in if you want to...
...start a business? Lithuania- a new EU country, Lithuania offers a lot for those with a budding entrepreneurial spirit, even if they don't carry a lot of capital with them. Start up costs are low, favorable legislation has been passed for business types of foreign extraction, and now is the time to get established before Lithuania introduces the Euro.
...live as near to forever as possible? Finland- a country tucked between Sweden and Russia, life in Finland is amazingly healthy. Finns eat well (lots of whole grains, fresh meats and fish, and seasonal fruits and berries) and are very active as a matter of course (most people I know in Finland bike or walk every where, and spend a lot of time with outdoor sports, like skiing). The air is very clean. People take sauna's regularly. If you can resist the lure of Finland's national vice (drinking copious amounts of alcohol), you're life expectancy should do better in Finland than anywhere else.
...party like a mad man? Spain- the disclaimer here being that you will first need to make some local friends (as they know the best places to go out) if you want to avoid the pitfalls of the tourist trap industry (you are coming to live, though, so that should take care of itself in time). The night life is amazing, more affordable than in other European countries, and truly goes all night.
...be able to smoke in as many public places as is possible? Russia- With smoking restrictions being put into place all over Europe (and indeed the world), smokers looking for refuge should continue moving eastward. True, there are other things to consider before a move to Russia (like learning the language, the standard of living, and having a former KGB agent as your president), but if being able to smoke your lungs out without fear of retribution is high on your list, look into Russia.
...become a gangster? Bulgaria- Bulgaria has run into problems with gaining entry to the EU because of the high levels of corruption and seedy 'businesses' within the country. Recent EU statistics state that around 14% of Bulgaria's judges are corrupt (taking bribes, etc.). This bodes great if you want to start an elicit business and become a gangster. All sorts of illegal trade (in drugs, human beings, etc.) moves from the east through Bulgaria to the European continent. Plus, once you are insanely wealthy, Bulgaria has some amazing beaches where you can head to relax and flaunt your wealth.
...avoid being totally ridiculed or worse for being an American? Ireland- This is the only, I repeat, ONLY country in Europe where, upon meeting new people and having my American-ness discovered, I was not instantly confronted with heated/pointed questions/comments about my countries greed/trigger-happy-ness/idiot president/imperialist nature etc. Usually, I was greeted instead with an, "Oh, America, I'd like to visit some day", or "I have cousins in America", or "You know, I visited (fill in name of state) for some time". It was great, and I have never really noticed how jumping the American hurdle used up a lot of my energy elsewhere in Europe.
...indulge your 'itchy feet' (a phrase used among travellers to denote a desire to keep travelling) on a whim? The United Kingdom- If you can't make up your mind as to where exactly in Europe you'd like to live, or if you want a base from which you can continue to travel the continent whenever you like, the UK is ideal. You can get a cheap flight to anywhere (practically) in Europe from the UK, and when you're resident there, especially in London, you will be surrounded by people from everywhere else in the world. For the constant traveller, there is no better city on Earth than London in which to settle down. Fellow travellers as well as immigrants of all nations fill the bursting metropolis. One need never be bored, and escape to somewhere else is only a Ryanair/Easyjet flight away.
This is but a short list of European countries. If your particular desire is not mentioned above, do not fret! There is something in Europe for absolutely everyone!