J.D. Meier did a post about some common application patterns for Windows Azure. Although I would not describe them as patterns myself (therefore they are too high level to really use them as a design starting point), they can be useful in presentations and high level discussions about the topic.
The covered scenario’s(patterns) are:
Pattern #1 - ASP.NET Forms Auth to Azure Tables Pattern #2 - ASP.NET Forms Auth to SQL Azure Pattern #3 - ASP.NET to AD with Claims Pattern #4 - ASP.NET to AD with Claims (Federation) Pattern #5 - ASP.NET to WCF on Azure Pattern #6 - ASP.NET On-Site to WCF on Azure Pattern #7 - ASP.NET On-Site to WCF on Azure with Claims Pattern #8 - REST with AppFabric Access Control Pattern #9 - ASP.NET to Azure Storage Pattern #10 - ASP.NET to SQL Azure Pattern #11 - ASP.NET On-Site to SQL Azure Through WCF