The first session that talked about Azure was (not surprisingly) incredibly popular. Filled a room that looked like it seated 700+ people. Then filled an overflow room. And the second overflow room is pack with people standing at the back.
The sample app is a thumbnail generator. In other words, a function that could normally be provided by a Windows Service. Interesting that the 'simplest' scenarios is that one. Interesting that it seems to indicate that what you're deploying into Azure is a service with ASP.NET or Silverlight as the user interface
A couple of times now, Azure has been referred to as an operating system.
Currently, the storage abstractions are: blobs for user data, simple tables for service state and queues for service communications. But these abstractions are not intended to replace a database. Astoria seems to be the expected CRUD channel.
"Azure is an operating system" is getting to the point where it should become a drinking game.
The second demo is a live site, managing teachers in Ethiopia. The speaking actually asked that we not to go to the site because it is live and the the typical usage pattern doesn't include being hit by 1000+ rabid developers all at once. :) In what appears to be a common approach, the user interface is a Silverlight communicating with Azure through web service calls.
As of noon (PDT) today, you can go to http://www.azure.com and download the desktop SDK. And publish applications to the close. Currently usage is free, with restrictions. And there is no indication yet regarding the pricing model, although in the keynote, Ray Ozzie suggested that it would be 'competitive' and that there would be support for 'hobbyists'. So look to Amazon's EC2 for a rough idea and figure that you will have some low/no cost option for you to play with.