Originally Posted by filtersweep
If you are a US citizen, and are not married to a citizen from an EU nation, and you are not sponsored by a company, you can largely forget about it. Most of the rest of the world pays back the US's arcane immigration policies in kind.
I recommend dumping your girlfriend and finding a hot Swede--- and I think they even recognize same sex marriages these days, so you could always switch teams.
Well, there aren't many countries (are there?) that will let you move there and live without already having a job lined up, regardless of where you're from (asylum excepted).
But yes, you need to find a job first. This is not that hard if you're in the right field. For example engineers (I'm one) are desirable in Denmark, so not only could I get a job here, but I get a discount on my taxes (from about 42% to about 33%, whoo-hoo!) because I'm in a 'desirable' field. On the other hand, Danmark has no need for more bakers, so don't waste your time trying to get a job as a pastry chef.
You can always find a job teaching English, but the pay will be pittance. But if you're young and looking for adventure, why not? there are also options to study here, but this is easier (I believe) as an exchange student than as a regular student.
What field are you in?