I'd have to consider the advantages to developing an application for Windows Azure. Windows Azure is a cloud platform that basically offers storage and the ability to host applications/services. Think of it as Microsoft's Platform as a service... A Windows OS in the cloud.
If, for example, I'm starting a Micro-ISV (independent software vendor - one man shop) who offers a web service, I would think that it offers me a few advantages. For starters, I would want my time and money, in terms of priorities, to go towards the web service I'm developing. So... I could utilize the Windows Azure platform, which essentially takes care of my IT needs, and concentrate on the development of the application. Windows Azure offers a 'pay as you grow' or 'pay what you use' model, so I don't have to worry about planning (storage, processing, scalability). I simply publish my web application to the Azure 'cloud' and it's available to the public. As the web application grows or shrinks, I pay for what I use and I can scale up or down as needed - it minimizes my IT management.
A couple of disadvantages that I'd have to consider...
You have to conform to the Windows Azure platform when developing. This can be both restrictive and requires a bit of a learning curve. If, for example, I'm creating a ASP.NET application, I would first have to download the Azure SDK and Visual Studio templates. Development can still be done in Visual Studio using C#/VB.NET, but let's just say the project setup is different, not necessarily hard, but some learning is required. Now, let's say my ASP.NET application requires a SQL Server database. Windows Azure offers Windows SQL Azure which is a relational database built off of SQL Server that supports T-SQL. For most routine applications, the difference between SQL Server and Azure SQL probably won't be a problem, but it'd have to be considered. Furthermore, you may lose some, perhaps all, SQL Server functionality with regards to SSRS, SSIS, jobs, etc (off the cuff, I do not know what it'd all be, but the functionality is a sub-set).
Bottom Line: If I've accepted the disadvantages and I know that they won't be a problem than the upsides to me are that I may have a cost effective approach to have a faster way to get out to the public, pay for what I use, minimize IT, but most importantly the ability to concentrate on the heart of the business (i.e. web service).