You can simply copy the favorites folder.
On Vista and higher the folder is “C:UsersUserAppDataRoamingSQLyogFavorites”
On XP and lower “C:documents and settingsUserapplication dataSQLyogFavorites” (as far as I remember).
Note that 'AppData' is a hidden folder unless you in Control Panel .. Folder options have chose to unhide hidden folders. Also on some systems some folders in the path may have localized names.
(and you could back up the SQLyog.ini too – your saved connections are stored here)