There's no shortage of places that want to sell you digital books, but Amazon's Kindle store is a relatively safe bet, considering that the company has built apps for just about every portable device out there.
The Kindle Android app features newspapers, magazines and books and synchronizes any of your other Kindle-enabled devices to the last page you read. The iPhone version knows the same synchronization trick, but it's still a books-only affair, as far as available content goes. Hopefully, we'll see newspapers and magazines added soon.
See also: iBooks, Barnes & Noble Nook, Kobo, Google Books, Audible