Have you noticed the street curbing (or curbs) lately? What is the material? Concrete, granite, marble, stone, or none at all?
I’ve pondered sidewalks before, but not really the curb material. Why bother to notice, you ask? From a transportation perspective, it’s interesting, because curbing is something specified in sidewalk and road construction plans. Curbs exist to protect pedestrians from traffic and to channel runoff.
Curbs typically exist in neighborhoods, villages, towns, cities, etc., as opposed to on stretches of highway and less dense areas of development. Their style, shape, construction methods, materials and age varies. Until living in Vermont, I never noticed granite curbing, which is popular (though not a rule) in recent sidewalk reconstruction throughout Vermont villages. Older curbs from the early 20th century are concrete. While home in New York recently, I noticed the curbs were either concrete or rough cut stone blocks with cement mortar. When living in North Carolina, I remember thinking it odd that in many neighborhoods, the lawn ran into the street without a curb, and many of the front yards were covered in (long leaf) pine straw in addition to grass. What is the reason for the difference?
I would guess climate factors into the decision, and availability of material. Vermont and New Hampshire are known for granite, and it is more durable for our harsh winters, road salts and other de-icing solutions and against plows. The climate in Southern Pines, NC was much milder compared to other places I’ve lived, and snow plows of any kind are rarely needed.

The older curbs in Vermont are often concrete, of varying composition. The smaller/less visible the aggregate (pebbles mostly), the newer the curb, is what I've found so far.
How about the height of the curbing? That factor depends on road speed and its correlation to pedestrian safety. Often, newer curbs will seem very tall (6-8 inches), whereas older curbs are very short. That is often a result of a different safety standards and/or how many layers of pavement have been applied over the years, thereby altering the height of the curb.
A lack of a curb also implies a less formal or a more rural development. I would infer that it is a less expensive method of road construction, since only road subbase and asphalt pavement is necessary, not curbs and sewer drain systems.
Curbs are a subtle element of the built environment and transportation system, but worth noticing because it could be an element that you never think of until it is different. Imagine how your town would look with different curbs, no curbs or the addition of curbs.

A good juxtaposition of concrete curb and granite curb with concrete sidewalk of varying ages, though all relatively recent.
Take a look next time you are out and about. If your town has a different curb, send me a picture! And if you really want to know more about curbs and all related features, read this chapter from the Federal Highway Administration’s guide to Designing Sidewalks and Trails for Access. Or read about curb ramps from FHWA.