It may surprise many to know that Royal Enfield was not the original name that the fable manufacturer operated under, as it was only a brand name. The full name was The Enfield Cycle Company Limited, from Redditch, Worcestershire, England. They sold bicycles and motorcycles, of course, but also lawnmowers and stationary engines. Many of the non-vehicular products they made were simply branded "Enfield".
Their first venture into vehicles was the Quadricycle, a four wheeled motorcycle powered by a De Dion steam engine. It didn't sell well, so in 1901 they produced a bicycle with a 239cc Minerva single cylinder engine on the downtube, and didn't look back from there. Early on in the 20th century, they were subcontracted by the Royal Smalls Arms Factory in Enfield, which is both where they acquired the Royal part of Royal Enfield, as well as came up with their slogan of "Built like a gun."
They famously produced the Royal Enfield Bullet, the longest-lived continuous production motorcycle in history, although after World War II, they started to run into financial troubles, as did many other motorcycle manufacturers. In 1967 they sold off their parts division to Velocette, and Norton Villiers took over as the main manufacturing arm, although by 1971, the Enfield Cycle Company went defunct.
However, by then they had established a factory and production arm of the Royal Enfield brand in India, as it was an emerging market, subcontracted to Madras Motors. The thing about it is, no one told the Indian operation that the main company shut down, so the sub-brand just kept on producing motorcycles. Once they learned of the Enfield Cycle Company's closure, they bought out the naming and licensing rights, and are the Royal Enfield that we all know today, keeping the legacy of the original company alive. Now they are widely known as the premier Indian motorcycle brand.
While a tumultuous history almost saw the brand fade into obscurity, it survived the collapse of the original company, and produces almost a million motorcycles per year nowadays. Since the mid-2010's, they've also turned around their reputation of being "cheap-n-cheerful" into being seriously good neo-retro motorcycles. These then, in our highly subjective opinion, are some of the best and most important Royal Enfield motorcycles (from either company to use the name) ever made.
Of note, prices will be listed in Pounds Sterling (£) up until the original Enfield went defunct, as Royal Enfield models did not sell particularly well in North America and finding accurate pricing data is very difficult.