When is noise a factor in basic analog circuits?
When evaluating an circuit’s performance for a low noise application, both internal and external noise sources must be considered.

External noise includes any type of external influences, such as external components and electrical/electromagnetic interference. Interference is defined as any unwanted signals arriving as either voltage or current, at any of the circuit’s terminals. It can appear as spikes,steps, sine waves, or random noise. Interference can come from anywhere: machinery, nearby power lines, RF transmitters or receivers, computers, or even circuitry within the same equipment (that is, digital circuits or switching-type power supplies).If all interference is eliminated by careful design and/or layout of the board, there can still be random noise associated with the circuit components.

Also for example there are internal sources of noise, take the case of an amplifier.

Noise appearing at the amplifier’s output is usually measured as a voltage. However, it is generated by both voltage and current sources. All internal sources are generally referred to the input,that is, treated as uncorrelated or independent random noise generators in series or in parallel with the inputs of an ideal noise-free amplifier.Flicker,Popcorn,Input referred and Output referred noise are some common internal noise in amplifiers.