Generally one doesnt "need" to have a polarized capacitor. What usually happens is one "needs" alot of capacitance. Some capacitor dielectrics offer more capacitance per volume than others. The ones that offer the highest "happen" to be polarized types due to the dielectric used. So with this type, a requirement of correct polarity on that capacitor is needed.
Which type (dielectric used) of capacitor depends on the application.
Sometimes one needs:
1) low impedance at high freq -> ceramic types good.
2) Really high voltage -> ceramic types also good.
3) Just lots of capacitance -> electrolytic types good.
4) Really low ESR -> Tantalum, ceramic types good.
5) Very good stability (temp-co, Volt-co) -> Poly types good.
and so on and so on
So it depends... how well does your capacitor need to perform? These answers will help you decide which capacitor type is best for the application.