A question for the hardcore travellers, having to do with visas

For all you hardcore travellers out there, you know, the ones who
take off and wander the earth, going from country to country in a
haphazard way, please tell me what the visa situation is like. You
see, I always thought that, at least in the USA, one had to apply for a
visa while they were still in the USA. Is it possible to just up and
enter a country while you're overseas, either without a visa or by
applying for a visa outside of the USA? Do you have to have your
passport stamped with all of the countries you might go to before you
even leave the USA?

Bradwell Jackson