Rob Newman and David Baddiel's stand-up. In the early nineties, they were the "New Rock 'n' Roll", hosting The Mary Whitehouse Experience and playing sell out gigs at Wembley Arena. Then they fell out, split their partnership, and a few years later most of their stuff fell by the wayside. Intellectual and philosophical comedy, and their grunge-meets-preppy style, was replaced by "laddish" comedy (including Baddiel's own Fantasy Football League TV show) and the Britpop wars of Oasis vs. Blur. Occasionally you might hear someone in Britain say "That's you that is!", but so far there has been no revival of interest. Both of them are now well known as authors, but their stand-up careers have been largely forgotten.
Rob Newman, anyway. David Baddiel's career recovered a few years later when he found a new partner in Frank Skinner. Skinner and Baddiel hosted the quirky sport programme Fantasy Football League and, with alt rock group The Lightning Seeds, scored a #1 UK hit with "Three Lions"...Then, Fantasy Football League was canceled and the bottom fell out of their career. Even though they can likely both retire from the royalties for "Three Lions", they've stuck around doing podcasts.
Andrew "Dice" Clay was a big hit in the late 80s/early 90s for his controversial, sexist insult humor (essentially the Don Rickles of his day). However, his act was seen as annoying and offensive to some (most notably Roger Ebert), mainly due to his tendencies to play his stage persona in reality, as well as the fact that being un-PC just for the sake of it was getting played out. The tipping point was the flop of his star vehicle film The Adventures of Ford Fairlane which, to add insult to injury, was removed from theaters due to pressure from Moral Guardians. Clay's popularity plummeted shortly afterwards; he subsequently tried to change his image as a result, even doing the failed CBS sitcom Bless This House where he played a family man, but to little avail.
On a more general note, such comedians as Bernard Manning and Jim Davidson, well known for their racist, sexist and mother-in-law jokes, were once huge, but are pretty much jokes themselves now.
Gallagher was huge in the The Eighties, selling out giant arenas and delivering expensive stage shows with a wide array of elaborate props. He fell quite far — until illness forced him to temporarily retire in 2012, he toiled in relative obscurity in local shows and squabbled with his copycat brother, while his act took an unpleasantly hateful, racist and homophobic turn (as described here). His original act is mostly remembered as being representative of all that was wrong with stand-up comedy in The Eighties.
Although they were not part of the Blue Collar Comedy group, similar Southern comedians such as Tim Wilson and Rodney Carrington had their downfalls around the same time. Unlike the Blue Collar guys, their acts were more diversified as they also recorded novelty songs and got some airplay on The Bob & Tom Show. However, Wilson's later albums got increasingly colored by his Libertarian political views, Carrington's high profanity level made him a harder sell after the post-Janet Jackson FCC crackdowns, and as mentioned above, Southern-flavored comedy was falling out of favor in general. Carrington tried to clean up his image some by starring in the sitcom Rodney, and his last two albums were composed entirely of songs (some of which were tamer and more serious than his prior efforts). He ended up scoring a Black Sheep Hit in 2009 with the soldier-themed Christmas song "Camouflage and Christmas Lights", but has mostly been quiet ever since. Meanwhile, Wilson continued to perform and record until he died suddenly of a heart attack in the first quarter of 2014.
Dane Cook was one of the most popular stand-up comedians in the mid-2000s, particularly amongst high school and college students (he was notably one of the first entertainers to use MySpace to build up a huge fanbase). By 2005-06, he had gained over 2 million MySpace friends and his CD Retaliation went double-platinum and became the best-selling comedy album in over 30 years. Then came the severe Hype Backlash from critics who were not amused by his comedic style (consisting primarily of observational humor and telling long-winded anecdotes) as well as hate coming from within the standup community, with numerous accusations of plagiarism and joke theft (most notably of Louis C.K.). This, combined with a few bad decisions in film roles (which were also critically savaged), the decline of MySpace, and Cook's own teengage fanbase outgrowing him all caused his popularity to take a major hit and he became more famous for his hatedom than his fandom. Unlike many of the above examples, Cook does continue to have some moderate commercial success (such as voice-acting in the Disney film Planes) although it is still only a shadow of what he had achieved at his peak just a few years before.
Jeff Dunham was once hugely popular with tons of merchandise and was praised for bringing new life into ventriloquism. Now he's mostly just remembered for his overreliance on stereotypes and rehashed material. Whenever he's brought up nowadays, it's usually in the form of a Take That.
His specials have been moved from Comedy Central to CMT, like the Blue Collar Tour before them. The televisual equivalent of going from Broadway to Branson.