Around here, we think the answer to that one is easy--EVERYONE should be trained in CPR and automated external defibrillator (AEDs).
There are some folks, though, who immediately jump to the top of the list, simply because of what they do:
Healthcare workers—If you have patient contact and work in contexts where CPR and first aid knowledge could be critical, up-to-date training may be required for you, and may include advanced training such as ACLS or PALS.
Lifeguards—You may be required to add oxygen administration to your emergency care “toolkit” along with CPR and AED.
Personal Trainers—Many fitness centers and gyms require an AED onsite and staff trained in its use.Employers with OSHA and other safety requirements--Some or all of your employees may be required to have training beyond CPR and AED, such as bloodborne pathogens and personal protective equipment training. SeeOSHA's Best Pracitces Guide: Fundamentals of a Workplace First Aid Program for more information.
Childcare Providers--There is not a single state that does not require childcare providers to be CPR certified.
School Personnel (including teachers, PE teachers, coaches, volunteer coaches, and bus drivers)--More and more states are requiring at least one onsite AED for each school in a district, with a requirement for CPR and AED training for all school personnel as well. It used to be the case that one person trained in CPR would be onsite during the school day, but our regulatory department is seeing a trend towards schools requiring training for all personnel onsite all day and those onsite for all afterschool activities (sports or non-sports related).