What header file replaced  in the Atmel ARM processors?
I think what you are looking for is the
CMSIS standard libraries (Cortex Microcontroller Software Interface Standard)

It is an abstraction layer that is vendor-independent and contains interfaces to the common registers, gpios, etc. For the Atmel, it is included in the ASF, but you don't have to use ASF, just take the CMSIS libraries, or you can download the CMSIS from the ARM website. Also, probably the IDE you are using has a wizard to create new projects that gives you the possibility to include them.
It is pretty much the standard interfaces in which every vendor library is built upon.