I have seen many textbooks that say consider a capacitor which is polarised (DC capacitors) and non-polarised capacitors also exist, but why don't inductors have AC inductors and DC inductors? Sorry for the silly question, but I want to know the answer.
There are inductors with polarity. They have a permanent magnet to bias the inductor opposite to the expected DC current. It's generally not worth it, but it has been done.
See, for example, DOI: 10.1109/ESTS.2011.5770892 Permanent magnet inductor design.
Abstract: Permanent magnet inductors (PMI) are useful in dc biased applications. They utilize the flux produced by a permanent magnet (PM) to partially offset the flux established by current in the inductor winding. The addition of permanent magnets allows for decreased inductor mass for a given inductor current and inductance rating. Herein, the Pareto-optimal front between loss and mass is established for a PMI inductor and is compared to that of a traditional EI core inductor. It is shown that the PMI inductor is significantly less massive than the EI core inductor for a given loss.
Polarized capacitors (which is a significant limitation on their application) are used because a polarized capacitor can be made significantly smaller and lighter than a non-polarized capacitor of the same value. If non-polarized capacitors were the same size, cost and performance as polarized capacitors of the same capacitance and voltage rating, there would be no reason to use the latter.
No this is an interesting question and I learned things myself while answering this question :) There are some instances where inductors may be polar sensitive. For instance, let's look at mutual inductance.
Credit goes to Fundamentals of Electric Circuits (6th edition) by Matthew Sadiku, chapter 13, page 557.
As you can see, polarity does matter when you're talking about transformers and mutual inductance. But this is more of reference polarity and magnetic field polarity. But you place the inductors upside down and it won't change anything. In other words, the inductors themselves don't have polarity.
In the case of regular inductors that are not meant to be used for its mutual inductance, it's just a coil... and no matter what direction that the current travels, it will always follow the proper path that the laws of physics define it to be. You can ask the same question about resistors. Why aren't resistors polar sensitive? It's because current travels the same way regardless how you place the resistor and the current behavior is always the same through the resistor. The same is true about an inductor.
As Iganacio pointed out, the reason why capacitors may have polarity is that of the material inside of a capacitor that defines it as polarization. On one side, there's dielectric material and on the other side, there's electrolytic material... You don't have that with inductors...
Maybe you are a bit confused. An inductor has no polarity until a coil of wire around it gives it a DC polarity because it produces a polarized magnetic field by using DC current, or use AC current of a frequency within the cores resonate range and you get an AC magnetic field of the same frequency.
Polarized cores for relays were tried for a few years then pulled from the market, as the pre-existing magnetic field tended to make them change state with extreme vibration on the z-axis.
If a core were pre-magnetized and a strong AC magnetic field was applied it would loose its pre-magnetized field and have no magnetic field unless AC or DC current flowed in the coil around it.
Inductors in general do NOT retain any magnetic field once the current is turned OFF. They are made of different materials than those used to make electromagnets or permanent magnets.
We can also remember that while capacitors are not theoretically polarised, though electrolytically formed ones fail if incorrectly connected so similarly a general inductor is also theoretically not polarised unless magnetically biased (well described in other answer).
However in practice they may be constructed in ways that require taking note of which terminal is which. Mostly this relates to the capacitive coupling to cores and cases or the electrostatic shielding from the outside casing or layers.
Ganged capacitors and mutual inductors are also polarised in relation to other sections of the component (as mentioned in other answer).