Some common types and packages of inductors are described here.
These inductors are the simplest type and are composed of just a few turns of relatively thick copper wire. The wire is enameled to insulate it from itself and prevent one long short across the whole inductor. Two of these are pictured on this simple radio transmitter board. Their inductance is generally low but they are very easy to make and tune.
The most common type of inductor in power applications has the wire wound around a ferrous core instead of just in open air. This is done mainly to increase the inductance greatly without using a whole lot of wire (which would increase cost). However, more energy is lost as waste heat with this type of inductor. An open surface mount design is pictured here on a battery management board. Many power inductors are more enclosed on all sides to increase thermal dissipation and increase shielding.
Wrapping the wire around a torus or donut shaped ferrous core is another way you'll see of making an inductor. Basically, the symmetric nature of these coils helps reduce the electromagnetic interference that leaks into the near surroundings. This mid-sized one came from a power supply and allows for a smaller, more efficient design than if it was one tall core.
Chokes are a type of small inductor that can come in several packages. This is a small component from an LED lightbulb driver board. They are named for their ability to "choke" higher frequency alternating current (AC) and smooth out power.
Now, the previous examples are really only seen if you look at circuit boards closely and identify them, but most people have probably seen something like this on a computer power cord. Ferrite bead inductors form a type of choke and are frequently put near either end of a power or data line such as a USB cable to reduce interference. They are effective both at blocking the cable from radiating electromagnetic interference (EMI) that can cause harmful effects to other equipment, and also at preventing the long cable from acting as an antenna and picking up stray EMI which can negatively impact the signal and lead to corrupted or slow data transfer.