Well, there are many materials that bypass the liquid state. It is all a matter of pressure, temperature and material.

For example, even water ice will sublimate.

Try this experiment. Fill up an ice cube tray in the freezer . Then leave the tray in the freezer and watch its progress for weeks and even months. BE PATIENT. Because the humidity in the freezer is so low ( true if you are not opening the freezer a lot and letting moist air in). You will notice over time that the ice volume in the tray will decrease through time! That is because the vapor pressure of H₂O in equilibrium with solid crystalline ice exceeds that in the freezer box. You see, the way the freezer works is to take warm moist air in, and then via the refrigeration cycle, it cools and de-humidifies the air... and that cold dry is used to chill everything in the freezer.

Every solid material exudes off an equilibrium vapor pressure. For most materials is far below the atmosphere pressure. But for a few, it is higher. And that is the case for the example you cited.

Actually the list is larger that the two things you named, but iodine is the other common material that goes from solid to gas without going through a liquid. Remember that this is at normal pressure, and under conditions where you change the pressure, the story might be different.

The process you are describing is called sublimation, in which a substance passes from the solid to the gas state without first becoming a liquid. Actually, there are a large number of materials that will sublime; it is just a question of the temperature and pressure at which this will occur.

For example, water will sublimate if you lower the pressure and temperature enough. This phenomenon is often used to freeze-dry things. Iodine will sublime at room temperature if you lower the pressure just a bit.

If you want to be more quantitative about it, you can look at the triple point of a material.

On a pressure-temperature phase diagram, this is one pressure and temperature point. Below either the triple point temperature OR the triple point pressure, the material is capable of sublimation.

For example, the triple point of mercury, found in older thermometers, is roughly -39 o C and a pressure of 0.2 mPa, so, if you have solid mercury at -50 o C and 100 mPa, it should sublimate. Alternatively, if it were at 10 o C and 0.1 mPa, it should also sublimate.

There are a lot more than three, and it all depends on the pressure and temperature you are doing this under.

In central Antarctica, water ice evaporates directly into a gaseous phase, without going through being a liquid first.

What at room conditions sublimes? Anything that you can smell, but which is still solid, for one thing. You already bring up mothballs. Rubber is another example, although rubber doesn't evaporate to the point that a rubber band will exactly disappear. I'm not sure the example you're looking for, but there are multiple possible answers.