Like nearly every other technological field, space travel will certainly make rapid advanced, perhaps far more than we can forsee today. Every country from Brazil to India is embracing either a full-blown space program or, at the very least, space technology. Heck, even Nigeria and South Africa have their own domestically made satellites. And these are just the national efforts - as more and more capital is available privately, along with access to such technology, private corporations and even individuals benefactors are tapping into this market (we've already had 3 full-blown space tourists). The chances for advancment in space travel will only increase as more nations become wealthier, most previously uneducated people go to school, and innovations compound upon one another to produce ever greater innovations still!
As for the will, there is indeed still a lot we care to explore. The moon alone is expected to recieve a good 7 or 8 missions within the next few years by no less than 6 different countries (the US, Russia, Japan, EU, India, and China). Mars is increasingly becoming the subject of a next 'space race' for exploration. And as for the need for colonies, a likely reality given the issues we face today, efforts like the International Space Station are providing testing ground for what it would take to colonize and settle space (since terraforming Mars for human habitation would likely take at least a millenium).