If you don't want to use SQL server you can use Amazon's hosted Dynamo DB nosql database as a session store.
You'll need the AWS SDK. To install this from the Visual Studio nuget package manager console use the following command
Install-Package AWSSDK
You can then configure your sessionState provider to use a custom provider. You must specify the region and credentials, either a profile or an IAM access and secret key combination. By default this will create a table named ASP.NET_SessionState.
<configuration>
<system.web>
<sessionState
timeout="20"
mode="Custom"
customProvider="DynamoDBSessionStoreProvider">
<providers>
<add name="DynamoDBSessionStoreProvider"
type="Amazon.SessionProvider.DynamoDBSessionStateStore"
AWSProfileName="[PROFILE]"
Region="[REGION]"
CreateIfNotExist="true"
/>
</providers>
</sessionState>
</system.web>
</configuration>