Amazon's DRM'd ebooks can't be used on other devices (unless you crack the DRM, which is a great nuisance), but their non-DRM'd books can be used on anything that reads .mobi. The way to check is the ebook's "Device Limit" number--if it's "unlimited," the book doesn't have DRM.
You can get started with free ebooks from a lot of sites:
http://wiki.mobileread.com/wiki/Free_eBooks has lists of dozens of free ebook sites, both downloadable and read-online ebooks.
Some of the largest are:
http://www.munseys.com
http://www.feedbooks.com
http://www.manybooks.net
Baen Books has a free library of science fiction ebooks at http://www.baen.com/library/
Sci-fi author & copyfight activist Cory Doctorow releases all of his books as free ebooks at http://craphound.com/
http://www.teleread.org/free-ebooks/ is Teleread's list of free ebook resources.
http://www.smashwords.com is a self-published ebook store, but it has a lot of free and "pay what you like" books.