Where should I NOT use a GFCI or AFCI?
For all new construction residential dwellings the answer is not too complicated. 

For older homes with existing wiring the answer is not as easy.  A qualified electrician would need to assess the wiring conditions and even then only by trail and error could they determine if ARC-fault protection would be able to work.  In some cases using an ARC-Fault receptacle downstream may be an option, whereas a complete rewire of the existing branch circuit may be needed.

I've elaborated on the answer breaking it up into residential and commerical establishments for educational purposes. 

Residential AFCI Requirements


All habitable rooms that contain 120 volt 15 or 20 Amp branch circuits require ARC-fault protection. This includes kitchens, family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms, sunrooms, recreation rooms, closets, hallways, laundry areas, or similar rooms or areas.
Exceptions:


Bathrooms, unfinished basements, garages, and outdoors.
Fire alarm system installed in accordance with 760.41( B) or 760.121( B) is installed in RMC, IMC, EMT, or steel-sheathed cable, Type AC or Type MC, meeting the requirements of 250.118, with metal outlet and junction boxes, AFCI protection shall be permitted to be omitted. (This is mainly in condominiums and not so much in traditional houses.) 
Existing installations are not required to be updated with ARC-fault protection unless modification to the wiring is done.


Exception: AFCI protection shall not be required where the extension of the existing conductors is not more than 1.8 m (6 ft) and does not include any additional outlets or devices.




Residential GFCI Requirements


All 125-volt, single-phase, 15- and 20-ampere receptacles installed in bathrooms, even if the receptacle is part of the bathroom lights, or if you have a washing machine in the bathroom it too requires GFCI protection.
Garages, sheds, and accessory buildings located at or below grade.
All outdoor receptacles.
All crawl space receptacles.
All unfinished basements.
All kitchen countertop areas.
All dishwashers.
All pool motors,  spas, and pumps
All receptacles within 6' of any sink.
All boathouses
All laundry areas
Exceptions:


A receptacle supplying only a permanently installed fire alarm or burglar alarm system shall not be required to have GFCI protection.
Receptacles that are not readily accessible and are supplied by a branch circuit dedicated to electric snow-melting, deicing, or pipeline and vessel heating equipment shall be permitted to be installed in accordance with 426.28 or 427.22, as applicable.
Receptacles installed for disposals and trash compactors are not required to be protected by GFCIs. A receptacle( s) installed behind a refrigerator is installed to supply that appliance, not the countertop, and is not covered by the kitchen countertop GFCI requirement.





Commercial ARC-fault Requirements


Dormitory units are required to have ARC-fault protection.


Commercial GFCI Requirements


All 125-volt, single-phase, 15- and 20-ampere receptacles installed in bathrooms, kitchens, rooftops and outdoors, 6' from a sink, indoor wet locations, locker rooms, garages, service bays, and similar areas.
All vending machines.
All pool motors, spas, and pumps.
All electric drinking fountains.
Exceptions:


In industrial laboratories, receptacles used to supply equipment where removal of power would introduce a greater hazard shall be permitted to be installed without GFCI protection. 
For receptacles located in patient bed locations of general care or critical care areas of health care facilities other than those covered under 210.8( B)( 1), GFCI protection shall not be required.
Receptacles that are not readily accessible and are supplied by a branch circuit dedicated to electric snow-melting, deicing, or pipeline and vessel heating equipment shall be permitted to be installed in accordance with 426.28 or 427.22, as applicable. 
In industrial establishments only, where the conditions of maintenance and supervision ensure that only qualified personnel are involved, an assured equipment grounding conductor program as specified in 590.6( B)( 2) shall be permitted for only those receptacle outlets used to supply equipment that would create a greater hazard if power is interrupted or having a design that is not compatible with GFCI protection.