Can anyone still become an adventurer or explorer?

Yes if you work hard enough to accumulateenough money and free time you yourself can become an adventurer and travel the world. Of course this would be for personal experiences rather than discovering a new and distant land but that's hard to do now a days.

Here's some good places to start:

http://kentonandrebecca.com/journal/becominganadventurer.html
http://www.professionaladventurer.com/how-to-guide
http://volunteerecotravel.suite101.com/article.cfm/how_to_become_an_adventure_travel_guide