That's an interesting question, and the answer depends on how pedantic we want to get. While many might name the Flamingo as deserving of that accolade, when Bugsy Siegel opened what was billed as the "world's most luxury hotel" on December 26, 1946, it was actually called The Pink Flamingo Hotel & Casino. The following year it underwent a remodel and a name change to The Fabulous Flamingo. From 1974 it was then The Flamingo Hilton, until settling, in 1999, into its current incarnation as the Flamingo Las Vegas.
Had you submitted this question a mere couple of years ago, the answer would have been the Sahara, which opened in 1952 and operated under the same name until it closed in May 2011; while it's about to be reincarnated, that will be under the SLS Vegas moniker.
So, the accurate answer to your query would be the Riviera, which debuted as the first high-rise on the Strip back in 1955. As to the remainder of the top three, while the Tropicana opened in 1957 and still operates on its original site, following the lawsuit brought by former owner Columbia Sussex in 2009, over the rights to the Tropicana name, was settled in 2011, the Las Vegas property began operating under the name Tropicana Las Vegas (to distinguish it from the Tropicana Atlantic City) and now, following the $165 million upgrade it received in 2009-11, dubs itself the "New Tropicana Las Vegas." Still, we're not sure for how long it can accurately designate itself as "new," and perhaps we're splitting hairs on this one.
If you don't count the Trop, then as far as originals on original sites are concerned, the next survivor is Caesars Palace, which opened in 1966, followed by Circus Circus, in 1968.
The terms by which your question is defined are, of course, particularly apposite when it comes to the Strip, for while several current casino names date back, what is currently the MGM Grand was formerly the Marina, while Bally's was the original MGM Grand, but prior to that was the Bonanza. The shuttered off-Strip Key Largo was called La Mirage in an earlier incarnation, not to be confused with The Mirage today, which is built on the site of what was formerly the Sans Souci, among many other things. Confused? Yes, we figured! Still, it's reassuring that Slots-a-Fun, which openened in 1979 as the smallest casino on the Strip, and the only one without a hotel, still operates as the inimitable Slots-a-Fun today.
To give a graphic impression of how much and how frequently Las Vegas Boulevard South has changed over the years, check out the maps and photographs below, which illustrate the evolution of the casino lay-of-the-land from 1950 to the 1980s.
