I think it depends on how you set up your MSN. All my conversations are automatically stored under My Documents>My Received Files Then there is a Folder with your name and a load of number which will contain a history of all conversations you have had. It also has a separate folder with names of all users of MSN on the one computer.
Hope this helps.
By the way its handy if your kids or partners dont know nothing about it. Errr nice to keep a check!