The Problem
You want to find out what you can adapt a particular object to, using the adaptTo(Object.class) method.
The Solution
Go to
http://localhost:4502/system/console/adapters and have a look for the class in the first column, Adaptable Class.
The next column provides all of the classes that you can adapt the originating class to, any conditions that may be imposed, and the bundle that provides the information.
So for example, if you look up
org.apache.sling.api.resource.Resource you will see that one of the listed adaptable classes is
com.day.cq.wcm.api.Page
Thus, if you start with a Resource resource, you can do:
Page page = resource.adaptTo(Page.class)
You could even create an adaption of your own. For example, if you have a Node object, you can create an AdaptTo mapping to map to MyCustomNode.
Further items of interest
How to create your own sling adapter.