It is really hard to imagine new competition being successful against Amazon at this point. They're truly so big that there are only about three or four companies in the world that could compete with them—basically Apple, Google, Microsoft, Exxon Mobil, and Berkshire Hathaway... and I'm not sure about the last three, and the first two don't seem interested.
Here are the main barriers to entry into competition against Amazon:
1. Near-complete availability. Amazon is pretty much the only site that can claim to be able to sell you very nearly any product ever manufactured. As a result, a sizable percentage of online buyers go straight to Amazon when searching for goods, which means that even if another store were better and cheaper, most people would never know.
2. Scale. Amazon's U.S. division sells more goods online (when measured by revenue) than all the other companies in the U.S. put together, and that number is growing pretty quickly.
Because of their high sales volume, they can demand deeper discounts on products than smaller businesses could, which means they can't realistically be undercut in price unless somebody is willing to operate at a staggering loss.
They also get special deals from the shipping companies that no new company starting out could possibly hope to get, which gives them another way to undercut any possible competition.
Finally, their scale means that they are able to do acceptably on what would otherwise be unsustainably low per-unit margins. Even if somebody else could manage to get all the same deals, without the volume, they'd never make enough money to break even like Amazon (almost) does.
3. Infrastructure. The amount of work required to create an Amazon replacement is staggering. Amazon isn't just a bookstore. It is also an online marketplace that anyone can use to list products and fulfill arbitrary products, an author/publisher interface for fixing metadata errors, a huge, highly automated system for order fulfillment (that brings costs down below what any newcomer to the industry could possibly hope to achieve), etc.
And that's just the physical product sales. Add to that the digital products and the hardware manufacturing needed to make those digital products useful, and it is pretty easy to see why competing with Amazon is a herculean task.