PADI Instructor Manual lists (1) only Cavern, Ice, Search and Recovery and Semi-Closed Rebreather (Dolphin/Atlantis) as requiring Advanced Open Water certification as a prerequisite. From 28 listed specialty courses, that is a tiny majority (4/28). Plus Tec40 and Tec Sidemount and also DM.
That said, the instructor may accept "proof of certification beyond entry-level (at least two certifications total); proof of 20 or more logged dives; documented experience in deep diving and underwater navigation"(2) in lieu of PADI AOW certification.
(1) 2013 PADI Instructor Manual, General Standards and Procedures, Summary of PADI Specialty Courses - Key Standards
(2) 2013 PADI Instructor Manual, General Standards and Procedures, Training Standards.
I was more referring to the PADI Pro Chain.
But from the specialties listed I would qualify Ice, Cavern and SCR as 'advanced' as opposed to such courses as the AWARE and Naturalist Specialties