From the outset, something was needed to counter the inhospitable climate around these parts to encourage settlers, and so from its earliest days Nevada started establishing itself as a renegade state that would permit things other states would not. Prostitution became legal in the mid-19th century and was actively practiced in the Block 16 area of the embryonic downtown Las Vegas area, for example, where it flourished until hit by the gambling ban of 1910.
Meanwhile, in the late 1890s and early 1900s, bigger cities including Reno, Carson, and Goldfield gained national attention when they hosted a handful of heavyweight championship boxing matches, at a time when prizefights were banned in most other states.
It was divorce, however, rather than either of the above, or the inception of legalized wide-open gambling a few decades later, that put the Silver State on the map as a scandalous place, with Reno, rather than Las Vegas, being the original "sin" city.
Prior to the twentieth century, divorce statutes in most states were extremely strict (in South Carolina it was not permitted at all), with residency requirements measured in years and severe physical abuse not always being considered adequate grounds for dissolving a union, for example. Hence, couples either chose to endure the misery of an unhappy marriage or were forced to make pilgrimages to one of the few states with more lenient laws. By the early 20th century these included Arkansas, Wyoming, Idaho, and Nevada, which vied for the migratory divorce trade by lowering their residency requirements. (Indiana had previously been included and was dubbed the Midwestern Sodom for its relatively lax statutes, with couples flooding in to obtain divorces on any grounds that a judge ruled "proper." In 1859, however, the legislature finally voted to require a year’s residency before allowing a divorce suit to be heard, effectively removing this state from the list.)
Nevada's marriage and divorce laws were established with the first territorial legislature in 1861 and carried over with little change when Nevada became a state in 1864. The residency period necessary to be a bona fide citizen was set at six months and seven grounds for divorce were allowed.
Relatively minor changes were made to Nevada's divorce law through the end of the 19th century, but then, in 1906, a society lawyer in New York, where divorce was permitted only on the grounds of adultery—which had to be proven in open court—hit on remote Nevada as the perfect place for his high-profile clients to dissolve their marriages -- or get "Reno-vated," as the saying went -- away from the public spotlight. Overnight, Reno went full-on into the marriage-dissolution business, with hoteliers, brothels, and private homeowners cashing in by providing temporary lodging to those waiting out the residency requirement.
In 1927 the state legislature lowered the residency requirement to an unheard-of three months, and then in 1931, in the same year that gambling was legalized once more in response to the economic impact of the Great Depression, the requirement was lowered once more to what elsewhere was considered an outrageous and scandalous six weeks -- making it the most lenient divorce law in the Union. The radical move helped Reno to survive the nation's economic collapse and in the decade of the 1930s, more than 30,000 divorces were granted at the Washoe County Courthouse, while by 1940 Nevada accounted for 49 out of 1000 divorces in the United States.
Today, the residency requirement (for at lease one spouse) remains at six weeks, with the divorce becoming final after another six, although today Nevada is a no-fault divorce state, making the law that much more liberal and non-intrusive. Just as in othre ways, Las Vegas has long eclipsed Reno as the state's divorce mecca, of course, although the number of divorces granted per annum was in decline the last time we saw any statistics.
As an aside, while we're still considered the "quickie-divorce" capital, bear in mind that Nevada is also considered a "community property" state, which means that most prenuptial contracts are void and that spouses are expected to share equally in joint assets (those obtained after the union). In other words, half of that lottery you won last week, half of the ancestral mansion you inherited while married, and half that Maserati you splurged on with your recent gambling winnings automatically belong to your other half, while half of his/her debts belong to you.