We created an entire SAAS application suite in Azure, and for the most part have been happy with the platform. We also migrated our existing on-premise applications to Azure as well. It has limitations that we continue to struggle with, but we have found workarounds to achieve what we need to do for the most part. We have been using it for about 3 years now, so we have got to feel a lot of growing pains along the way.
We have a combination of Azure VM's running SQL Server (for legacy apps that we didn't want to or couldn't convert to Azure SQL), VM's for SSIS, VM's for SSRS and Azure SQL databases, in addition we have web roles, worker roles, blog storage, table storage, etc... We are currently looking to start using Azure Data Warehouse. I try to stay on top of the new features that are constantly being released, some are good, and others are just eh, not good. We still don't have a good replacement for SSIS or SQL Agent jobs, or being able to answer that question we always get "Why is the database slow?"
We use a shared multi-tenant database architecture, so we don't have shards. We may need to use them due to size limitations as some point.
As a long time SQL server DBA, I wasn't thrilled about the decision to start using Azure SQL database, but I've learned that it's not all the bad. I figure it's been a good experience learning the new technology and will only make me a better DBA. Lets face it cloud adaptation is only going to continue to grow.