Lord Of The Rings: The Subtle Connection Between Smaug, Hobbits, & The Riders Of Rohan
There are many characters in Middle-earth and while some of them share stories, others operate half a world away. Smaug the Golden and the Riders of Rohan fall into the latter category. The mighty dragon inhabits the Lonely Mountain in the northeastern corner of the Middle-earth map, where he plays a key role in "The Hobbit," and the Rohirrim dwell in the opposite corner of the continent, where their principal activity is helping their Gondorian allies in "The Lord of the Rings." However, if you go back far enough, the two disparate elements of J.R.R. Tolkien's legendarium are actually connected ... in a small way.
In "The Hobbit," Thorin explains where Smaug came from to Bilbo, saying, "There were lots of dragons in the North in those days." The appendices in "The Return of the King" also explain the backstory of the Rohirrim, describing their original homeland thusly: "That land lay near the sources of Anduin, between the furthest ranges of the Misty Mountains and the northernmost parts of Mirkwood." Vague geographic descriptors aside, this roughly translates as the same area where Dragons (eventually including Smaug) come from.
A bit later, the "Return of the King" text says that after they migrate south, the Rohirrim continue to remember their northern home, adding the juicy tidbit that one of their heroes, Fram, "slew Scatha, the great dragon of Ered Mithrin, and the land had peace from the long-worms afterwards." While Smaug's relatives and the Men of Rohan are estranged by the time of the "Hobbit" and "Lord of the Rings," they share the important connection that their ancestors dwelt in and fought over the same areas of land centuries before those later stories take place.
Théoden references his people's ties to the hobbits in The Two Towers
In J.R.R. Tolkien's "The Two Towers" novel, we get another cryptic reference to the Rohirrim's past from King Théoden, but in this case, it doesn't have to do with Dragons, but with Hobbits. When the King of the Mark meets Merry and Pippin in the rubble of Saruman's Ent-smashed dwelling, he tells them, "My people came out of the North long ago," adding that they still have ancient tales about Halfings, or "Holbytlan," as they call them.
However, the friendly king clarifies that these are merely legends. "But I will not deceive you: we know no tales about hobbits." He explains that the little they do remember is that they are believed to be a short-statured folk who hide from Men and don't do much (which sounds like it may have been an inspiration for Amazon Studios's proto-Hobbit Harfoots).
It's understandable that, after half a millennium, the Rohirrim would have forgotten about a half-sized race of sheepish, hole-dwelling Halflings. At the same time, the reference to "the North" clearly hints back to the epic origins of Théoden's people — a beginning that they still remember includes dragon slaying and fights for survival before they finally headed south, quite literally looking for greener pastures.