Those vessels sailing out into the unknown, they weren't carrying noblemen or aristocrats, artists or merchants. They were crewed by people living on the edge of life: the madmen, orphans, ex-convicts, outcasts like myself. As a felon, I'm an unlikely candidate for most things. But perhaps not for this. Perhaps I am the most likely.
How much truth is there to this quote? Were the majority of people living in colonies and attached to explorations from society's underbelly, or were they well-adjusted, ambitious, go-getters?
I don't have a general answer, but I have some specific examples of those who had a choice to go exploring and did: Edmond Halley, who was exploring the oceans in the 17th century, Joseph Banks, who traveled on James Cook's first voyage in the 18th century, and Charles Darwin, who traveled on the Beagle in the 19th. All three were gentlemen--adventurous, certainly very curious, perhaps a little out of the ordinary (they would have to be) but sane gentlemen.
Edmond Halley, from a wealthy manufacturing background, undertook sea voyages to carry out scientific and astronomical work (his first being in 1676, when he was 20). He even captained (by many accounts poorly) his own ship in order to carry out research into compass variations in the Atlantic ocean. He did these things as part of his career in England, not inspite of it.
Joseph Banks, voyaging in the later half of the 18th century, was also a young, wealthy and in his case landed gentleman (22) when, since he had nothing else to do and an urge for adventure, booked himself on a scientific trip to Newfoundland and Labrador. Four years later, he was appointed botanist on James Cook's first voyage--one which famously took in what Tahiti had to offer. The trip was definitively off the map, going to places completely or almost completely unreached by European explorers. But it was still heavily populated by gentlemen who had scientific interests. Later, his own travelling days done, Banks founded the early Kew collection of exotic plants, receiving samples from other naturalists around the world sent purposely to find samples of possible use.
Charles Darwin famously was not the naturalist on FitzRoy's Beagle, but his assignment to the expedition was not unlike Banks'. Both were young at the time, and both were extraordinary in their natural interests, and both did not quite fit a leisurely or mundane life. However, like Banks, Darwin was level-headed and sane enough to be allowed along as FitzRoy's companion on a ship where gentlemanly company would be somewhat otherwise limited.
All three of these men went off sane and came back perhaps slightly less sane. All of them were not accidents or outliers, but examples of the heavy scientific and completely level-headed exploratory impulse among polite society. After all, expeditions like this take money. You don't fund an expedition which has an increased chance of failing because the people associated with it are known to be unbalanced. You fund an expedition which has at its head a great leadership team who can deal with incredibly poor conditions, unexpected occurrances and diplomatic disasters, and still bring back useful information whether it be something tradeable, or something growable, or something that can be invaded.
My answer? I can't speak for who the sailors were, but I think the vessels sailing into the unknown were led by people who if they weren't precisely entirely well-adjusted (there is a reason they went, after all) had something important to offer and were trusted or otherwise recommended to deliver on an incredibly difficult enterprise.
Sources:
Richard Holmes' The Age of Wonder, and my own general knowledge of Halley and Darwin from earlier research and reading. Darwin Slept Here is a very interesting easy-reading book into Darwin's time in South America.