Or do you need to have a job or spouse/family waiting for you, etc?
That depends. Every country has different requirements for immigration.
As a US-Citizen, it is usually no problem at all to move to any European country and study at a University for a year or so.
If you want to work there, you need a working permit. If you work for an international company and they send you abroad for some years, also no problem.
If you want to move somewhere and stay there for good, you need to have either that countries citizenship or an unlimited residence permit.
I'm not really into those things, but I expect that a US-American or a Canadian can get that much easier than a person from any third-world country.
If you really want to know for sure, surf the countries embassy sites for more information.
It depends on your nationality. European Union (EU) citizens can move to France - I from the UK but have lived in France for 10 years now. You are in Canada I see - if you are Canadian you will have to research the entry requirements for a Canadian citizen to live in France (or whichever country). If you are and EU citizen currently living in Canada, or (I think) have a parent who is an EU citizen, then you can move to France quite easily.
It depends, because you can't just move anywhere. There is a long list of things you will need before just moving to another state, let alone new country/continent all together. You need to know the history of the place, how to convert your money from US dollars to whatever their currency is, the language, how to be polite and how do and say certain things that aren't offensive, and things you shouldn't do to get into jail.
If your at an adult age, have all your pappers in order and everything, somewhere to live and stuff like that, then yeah, why not?
You also need a passport and citizenship if you are going to be living there, correct?
It all depends on your passport!