I recently wrote some logic that would delete old files from Azure Blob Storage programatically and I thought that I would share it with you guys. In the method below, you can specify the type of files you want deleted, as well as the number of days you wish to go back (e.g delete all files that are `.zip` files in the last month).
/// <summary>
/// This method removes files from Azure Blob Storage based on the below criterion
/// </summary>
/// <param name="contentType">The MIME type</param>
/// <param name="ageLimit">The number of days to go back</param>
public static void DeleteOldBlobFiles(string contentType, int ageLimit)
{
	try 
	{
	    var storageAccount = CloudStorageAccount.Parse("CONNECTIONSTRING");
	    var client = storageAccount.CreateCloudBlobClient();
	    var container = client.GetContainerReference("CONTAINERNAME");
	    var blobs = container.ListBlobs();

	    foreach (var item in blobs)
	    {
	        if(item.GetType() == typeof(CloudBlockBlob))
	        {
	            var blob = (CloudBlockBlob) item;
	            var lastMod = blob.Properties.LastModifiedUtc;
	            var contentType = blob.Properties.ContentType;

	            // mime = "application/zip"
	            if (contentType == contentType)
	            {
	                if(lastMod < DateTime.Now.AddDays(-ageLimit))
	                {
	                    blob.Delete();
	                }
	            }
	        }
	    }

	}
	catch(Exception ex)
	{
	    // Do custom exception handling logic
	}
}
You will need to download the Azure SDK in order to make use of the Azure Storage classes used in this code example. Hope somebody finds this useful!