Make a field specific to a user I would like to make a field that is specific to a single user, similar to a
non-global flag but allowing more field types than just boolean. Is there a way to do this? For example, if User A sets this field on Node B to 5, then User C looks at that node, he won't see User A's value. If User C then edits the field to another value, then he will see that value instead, and User A will still see his value of 5.
Yes, you can add fields to the user entity with the Field API to 

Admin > Config > Account settings > Manage fields

The variety of field types are available and each user has their own field value