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Heh, no I don't think many scientists aspire to get a nobel prize, its one of those things that are much too huge to aim for (though maybe not, just not something I've ever heard anyone say.. maybe they do!).
Depending on the research many do it for the sake of curiosity, the hunger to learn more and understand more. To step out into the unknown. I research because I believe it will make a difference to the natural environment. I like to think that I'll make a difference, whether it be now or in the future. (And I'm probably the most curious person alive).
Some do it for the "fame" by getting published in high end journals (like nature and science) though I'm not sure how many people think like this as it takes alot to get into such journals.
Some might do it for the money, depending on your career I'm sure there are some high paying research jobs.
Almost no scientists can pretend to get the Nobel prize. This is even more true at the beginning of a carrier. I also never heard anyone claiming he would aspire for it.
Some may aspire to make money. And a lot of research is done with that idea in mind (think of research done in pharmaceutical companies).
The main reason (hopefully) is the quest for understanding. It is a strong motivation per se. Knowing you are doing something nobody did before is actually rewarding.