Longest-running talk show in US history. Each hosting era distinguished by its own title and branding, but officially all versions are known as The Tonight Show. The IMDb link is for the current incarnation, The Tonight Show Starring Jimmy Fallon.
Eras:
Tonight (1954-1957): hosted by Steve Allen, with Ernie Kovacs joining as alternate host 1956-1957
Tonight! America After Dark (1957): short-lived attempt at turning Tonight into a news program. Hosted by Jack Lescoulie and Jazzbo Collins.
Tonight Starring Jack Paar (1957-1962): also known as the Jack Paar Tonight Show or simply The Jack Paar Show during this time.
The Tonight Show (1962): six-month interregnum with no permanent host while Paar's appointed replacement waited out a contract with another network.
The Tonight Show Starring Johnny Carson (1962-1992)
The Tonight Show with Jay Leno (1992-2009; 2010-2014)
The Tonight Show with Conan O'Brien (2009-2010)
The Tonight Show Starring Jimmy Fallon (2014-present)
Some interesting trivia to add: Carson actually got his start on the Tonight Show several years before becoming host as he served as guest host for a while under Jack Paar (Paar was the one who introduced both that aspect of the show and dedicating Friday night to reruns both of which were continued by Carson). The 1962 "interregnum" as noted featured a number of temporary hosts. According to Wikipedia some of them thought they were trying out to replace Paar even though Carson had been chosen, and Jerry Lewis apparently did so well NBC nearly changed its mind on Carson and gave the show to Jerry instead! Merv Griffin also hosted for a bit during that period and that was apparently the catalyst for him becoming a talk show host. Arlene Francis, known as a panelist for What's My Line, was another temporary host, reportedly becoming the first woman to host a late-night talk show in the process.
@GimmeVinyl Fortunately many episodes of Groucho's game show You Bet Your Life survive. It was actually a talk show disguised as a game show, so we can get a good idea of how he might have handled Tonight. Sadly, most of the Tonight Shows prior to about 1970 have been lost over time. Remarkably, most of the first Steve Allen episode survives, as does audio from the opening of Carson's first show, featuring his first monologue. But complete episodes from the 1960s, both Paar and Carson, are not that common. Fortunately one surviving clip - and one of the only 1960s ones in colour (most survive as B&W) - is from about 1965 and features Groucho as a guest.
Ok.. during 1962, between the time Jack Paar left the show, and Johnny Carson finally took the helm, one of the guest hosts that did several shows was Groucho Marx... Oh, I would have loved to have seen that...
The way I handled the Tonight Show may be a bit controversial, but I chose to treat it as one long series because that's what it is. During its various eras it took on branding to promote the host of the day, and for a brief time it changed format to become an evening version of Today, but it has always been The Tonight Show (though early on it was just called Tonight). I have attempted to locate the title card for the first incarnation of the show - amazingly the very first episode from 1954 still exists and features Steve Allen prophetically predicting that the show "will go on forever". But given the context of this entry I don't know if the current Jimmy Fallon title card might be a better choice?
EDIT: Here is the clip in which Allen (who is actually referencing the running time of the show, but it's easy to look back with hindsight) predicts that Tonight will run forever.