The first in the list is of course Steve Jobs.  Jobs was looking for ways to push his Macintosh computers, since he has always lacked market share compared to PC computers.  Who exactly came up with the 'music player' idea is unknown, it was probably a collaborated effort, but Jobs wanted to pursue it.

Jon Rubenstein can be credited to putting the initial pieces together.  He did a lot of the research to see if such a device was even feasible, in which they quickly found that it was.

Finalizing the product was in the hands of a man named Jonathan Ive, and he's not only the lead designer of the iPod, but the iMac as well.

Jonathan and his team came up with the prototypes and tweaked the product into what you see today.  Jonathan doesn't like to give himself credit though, he points back to Apple as a whole and likes to give everyone in the process credit for all of their hard work into putting together the final product.