Today CRM Online is available as service from Microsoft. Yes the name has changed from Dynamics CRM Live to Microsoft Dynamics CRM Online (Not to confuse too much on the existing www.live.com platform targeting more the consumer and smaller business) The product code base is more or less the same as the on-premise version and you can still access the rich web service interface even if you implementation is on CRM online. Of course you can add your own custom entities, attributes and relationships to extend the already out-of-the-box functionality. Checkout Extensibility Features CRM Online vs. On-Premise in Microsoft Dynamics CRM 4.0 for all the details http://msdn2.microsoft.com/en-us/library/cc299424.aspx

Check it out at http://crm.dynamics.com/

Press release http://www.microsoft.com/presspass/press/2008/apr08/04-22DynamicsCRMOnlinePR.mspx

CRM Online technology overview http://crm.dynamics.com/technology/index.html

Authentication explained from custom .NET code http://msdn2.microsoft.com/en-us/library/cc151051.aspx