I've received a number of requests for Windows Live Mail invitations recently, due to my recent post offering up Windows Live Messenger account invitations. I don't have any Live Mail invites, but I'd suggest you sign up here and see what happens. At least one person to whom I suggested this signed up today and received his invitation today, as well:

http://ideas.live.com/

(Windows Live Mail is the new version of Hotmail, currently in beta test mode and available only by invitation, which you can sign up for at the above addresses)