A polarized capacitor must have a dc bias on it, and in the presence of an ac signal, it must remain biased. Both capacitor types could be used in any circuit, but in the case of the polarized capacitor, the circuit may need rearranging in order for a dc bias to be applied to the capacitor. The transition between capacitor types is in the range of 0.1uF-100uF.
Which type is used is governed by the value required, and the physical and electrical properties desired of the capacitor. Below 100uF there are typically paper, film, and ceramic types, non polarized, and above .1uF, tantalum and aluminium polarized capacitors are most common.
Cheers,
Richard
