What are the best old electrical appliances to extract electronic components from?
Most electronic devices have a range of components. The following are mainly those that are somewhat more special or useful.

Many parts for Robots will be easily  sourced from surplus material.
Drone motors usually need high power per volume and high power per mass and often existing motors will not be adequate. Rewinding of some motors may be possible. 

Printers are often a source of small electric motors. Also possibly solenoids, drive belts, mechanical and electromechanical parts &amp; position sensors. Some have mains to low voltage power supplies fitted internally. 

Dead (or alive) CFL lightbulbs provide high voltage (mains rated) transistors  

LED light bulbs have AC to lower voltage DC conversion circuits but the end voltages may still be quite high.

Some but not all toasters can have timers, solenoids (to release the mechanism if power is removed).

Many consumer main powered portable device provide housings for construction and mains input to low voltage DC power supplies BUT be very careful that supplies are mains isolated on the low voltage side - many many not be.

PC/computer power supplied have high voltage transistors and capacitors and noise filter magnetics and mains rated non-polarised capacitors.

Microwave ovens have magnets, turntable motor, interlock switches and the main transformer which is useful but somewhat unusual in its magnetic design - designed to have a saggy output under load. Be aware that the magnetron MAY use fatally dangerous Beryllium ceramic insulator due to its high thermal conductivity.

Be aware that SOME older transformers and high voltage non polarised capacitors MAY use carcinogenic PCB oil for internal insulation and thermal transfer. Not so common.

Televisions contain just about everything :-) - except maybe motors.

TVs, radios and much else are good sources of surface mount components. Learn how to desolder them well. A fine tip iron is usually NOT what is needed. 

Direct drive washing machines may use high power brushless DC motors useful as seriously powerful motors or for wind or water turbines. 

CD &amp; DVD players contain motors which MAY be able to be rewound to have far greater power than originally.

Many more ...