Recently we had a client that was experiencing a log in loop for Dynamics CRM Online 2011. Basically, when the client would try to log in via the web portal - the webpage would just continue to loop through a series of webpages - never giving the user the opportunity to actually log on with their Windows Live ID (Microsoft Account).
After reviewing the settings - we determined that the internet settings for IE had been recently reset. We added *.dynamics.com and *.live.com to their trusted sites (Tools-Internet Options-Security-Trusted Sites). After adding this and restarting IE - the client was able to log in just fine.