It depends where you are asking about on both counts. For instance, if you look at Great Britain, dueling declined by the mid-19th century, while in Latin America the heyday of dueling only really began in the late 19th century, and its popularity there lasted several decades into the 20th, not entirely petering out until startlingly recent, the last (known) duel in Uruguay being fought in 1971 (more on this here).
"Common" is also a tough word to parse, as what would you consider to be many duels? Simpson, for example, found records of 840 duels fought by Brits between 1785 and 1850, which comes out to a bit more than a dozen per year, but while to me that sounds pretty reasonable, it is hard to say whether you'd be over- or underwhelmed by it! To put a little context though, consider several factors, the first being that many more duels were likely fought and we have no record of them. Duels, by their nature, were often done clandestinely, and especially when no one was killed or seriously injured, it wouldn't be newsworthy, so quite easy to just... not know it happened.
The second is that duels were part of a larger affair of honor, the final step in a ritualistic exchange of letters that, ideally, would prevent the duel from happening. People at the time estimated that only 1 in 10 affairs of honor -if not fewer - ended up as duels we know of for a year might mean twice that we have no record of, and 10 times as many disputes which were settled without pistols.
Finally, it is worth noting that the duelist was a member of the elites - Satisfaktionsfähig as the Germans called it (capable of giving satisfaction) - and only a fraction of the general population. The population of potential duelists was perhaps 1 to 5 percent of the population as a whole. If we look at New York City, for an example, Joanne Freeman found records of 16 affairs of honor from 1795 to 1807 in her study of the phenomenon in the Early Republic. In a city of 60,000 people, that meant that the Satisfaktionsfähig numbered maybe 1,500 men. 16 affairs of honor, involving a minimum of 4 people (two principles, and two seconds), means probably 4-5 percent of elite men in NYC were involved in an affair of honor in the period, and those are the ones we know of (I of course am assuming it wasn't the same men over and over).
Finally, it needs to be put in broader context. The British fought (at least) 840 duels over a 65 year period. The Italians fought (at least) 3,918 duels over a 20 year period, from 1879 to 1899, based on the records of Jacopo Gelli. But Gelli recorded 20 deaths, while Simpson recorded 229, an order of magnitude more for a fraction as many encounters. The important factor here is how national styles differed. The British dueled with pistols, at decently close range, and while the rules of the duel were intended to mitigate skill, sheer chance ensured many were struck, and killed. The Italians dueled with swords, and, as with the French in the period as well who fought with the same gusto, had little interest in killing each other outside of the rare serious encounter, the ritual of the duel being about masculine posturing. The duelists would prance about, get a few scratched on their arms, and afterwards shake hands and be done with it, usually with a write-up in the paper about how they were both men of honor (more on this can be found here).
This brings us to the other aspect of your question, and the decline of the duel. In Britain, the duel ended due to a mix of factors, but the social pressures due to the fatality rate is important. By the 1840s, it was seen as primarily contained within the military - that last bastion of honor - and a series of reforms were implemented to try and allow officers to refuse a duel honorably. Courts of honor were instituted, which helped some, and pensions were denied for widows of officers who died dueling, which provided a convenient excuse as well. The last fatal duel between Englishmen was fought in 1845.
Britain though was, if anything, the anomaly, with dueling ending through social pressure and reform, whereas most countries saw the duel end due to large, violent shifts in society. In the United States, the American Civil War is seen as the death knell of the duel, dueling surviving in the American South in some health up until the 1860s, and then quickly declining over the next few decades. It was hard to question the honor of someone who had served in the war, and especially for the younger generation, it seemed to be an institution not in line with the vision of the New South. The last notable duel, fought between two older men, both Colonels in the war, was fought in 1880 in South Carolina. It shocked the region enough to see the survivor prosecuted, and although acquitted, resulted in passage of a strong anti-dueling law, something that past duels had never managed.
Similar factors came into play in Europe, the Great War bringing to an end, or at least causing a quick decline, in dueling in France, Italy, Germany, and Russia, although not always for the same reasons, precisely. Russia, of course, had a revolution to end things, and dueling did continue for a bit within the White Russian emigre communities. In France and Italy, dueling didn't end immediately, but as with the US, it became less popular, the death and destruction of the war imparting something of a distaste for it with many. There was a brief surge in duels just after the war, as many officers had agreed to postpone disputes until the war ended which now had to be paid off, but on the whole, duels declined precipitously, although in France, they would occur occasionally into the 1960s, while in Italy, a brief resurgence in the early Fascist period (See here) kept it alive through much of the '20s, although by the 1930s they sought to end it, the practice dying there by WWII. Similarly in Germany, interest declined quickly, although it didn't entirely die out within the Army, and had some resurgent interest under the Nazis, but it was quite brief and caught between competing, contradictory forced (See previous link).