What about notification by email whenever it's your turn to move, not just when a new game starts? Of course, it should be something you could turn on and off as you like, and it should only send an email the first time it's your turn after you logged off, not 10 e-mails if it becomes your turn in 10 seperate games between logins.
I know it would save me quite a few unneccesary logins, and following disappointments.

What do you think?