Berlin, Germany: Took some savings from working back in the States, got here on a 90-day tourist visa, found an apartment and got my first working visa (without about 2 weeks to spare!, although you can extend a tourist visa here) as an English teacher. Later transitioned into a full-time development job.

Came here with my German girlfriend though, so I had a bit of help in terms of language, talking with bureaucracy, etc. But getting a visa (at least as an American!) was fairly straightforward and cheap, if occasionally slow and, well, bureaucratic.

Been here about 4 1/2 years now and love it.