Script Summary: Checks the Hotmail inbox for new messages at a specified time interval. A popup appears to alert when there are new ones. (NB. only works if inbox is open in a window/tab).
Default time interval 5 minutes. Set a different time using the User Script commands (right click on the monkey, select "User Script commands..." then "Set time interval to check for Hotmail messages...". Also, "Tools", "Greasemonkey", "User Script commands...", "Set time interval to check for Hotmail messages...").
I don't think there are any, but if you find any bugs, please post a description in the comments.