Not sure if this has ever been mentioned before, but I'll give it a go.
Basically, I was wondering if it would be possible for the My Games page of RHP to automatically refresh every, say 5-10 mins, or even every 30 mins. Not only this, but if the title bar at the top of the webpage (i.e. RedHotPawn.com - Online Chess)could be altered to reflect whether any games require moving in. This would be beneficial to people who leave a window or tab open on their desktop whilst doing other stuff, without having to manually refer back to the webpage every so often.
A similar thing is done on the Gmail inbox page - the tile bar changing to Gmail - Inbox (x) where x is the number of unread e-mails. Maybe the title bar could read "RedHotPawn.com - My Games (x)" x being number of games to move in. I have absolutely no idea how difficult this would be, or whether it would consume uber-bandwidth, but it was just an idea.
ps If anyone wants a gmail account let me know - i have loads of invites left.