I have just added the rating feature for my page layouts and is working fine. However I noticed that in order to do so I had to have the User Profile Service running. Is there a way to have the rating feature working without the User profile Service?
No, if you want to leverage out of the box rating feature, you must enable and use User profile service because rating data is stored in social database.
Edit [Based on comments]
As per http://technet.microsoft.com/en-us/library/gg188041.aspx, user profiles can be imported from supported directory services and enhanced (with extra properties) via data stored in external systems. Alternatively, you can create user profiles from external systems without synchronizing with directory services. Out of the box only authenticated users can rate the content. However, there are solutions our there which allows anonymous users to rate the content. For example: http://blog.mastykarz.nl/mavention-anonymous-rating/
Check out this link as well: http://social.msdn.microsoft.com/Forums/en-US/sharepoint2010general/thread/c2bf5040-107e-4a54-8cf6-be6927c4e0a6/