Funnily enough, I fantasize about a similar organization I call The Knights Tempura. We would travel through the corridors of time introducing Japanese-style deep fried food to all the iterations of reality.
Sell the Cabbage Patch dolls and walkmans I brought with me and buy Intel and Microsoft stock.
Foggy, thirty+ year-old memory coming up. And it’s not even about time travel! 
I seem to recall an old Twilight Zone or Outer Limits episode (it was definitely in B&W) where the story revolved around an older man telling a couple about his last boat ride, forty years in the past, that shook him so badly that it wasn’t until his fifties that he got on another ocean-going ship again. The boat he was talking about was, of course, the Titanic. Anyway, the story ended with the older man joking, saying something along the lines of “What are the odds of my being in two shipwrecks in a row?” or something equally damning. The couple laughed, they all walked away to reveal a ring bouy with “ANDREA DORIA” stenciled on it. (Or another famous wrecked ship, like the Morro Castle or something).
That was the seminal “Twilight Zone” episode. Rod Serling is said to have been inspired by the tall tales told by a retired seaman named Frank Towers, who claimed to have survived the sinkings of the Titanic and Lusitania as well as the Empress of Ireland.
Seperate episodes. In one, Quark co end up in Roswell. In the Voyager episode, Voyager is attacked by a psycho from the future who blames them for destroying the solar system; both are thrown into the past.
I’ve seen at least two stories ( Up the Line by Robert Silverberg, and a short story who title I don’t remember ) about time travellers who go to ancient disasters as tourists.
For the ultimate in rescue work, Spider Robinson has written several stories involving time travellers whose goal in to implant undetectable devices in the brains of every human who ever lived; upon death, these devices send the data comprising the mind to the future. There, they can be given new life; the goal is to literally save everyone who ever lived. Also, in his Callahan series several time travellers show up to prevent disasters ( at least two that would destroy humanity, and one that would destroy the universe ).
That’s it! Lusitania!
Thanks! 
Least useful to sufferers is The Knights Templeton, an order that travels to the 14th century and teaches the plague rats to imitate Paul Lynde.
I believe it was Steven Wright (though I could be wrong) who made a comment to the effect of “There’d really only ever need to be one convention for time travellers.”
PS- I’d go back and take automatic weapons to Nat Turner as well, but in so doing I’d probably blink my ancestors (and therefore myself) out of existence.
They actually had one at Harvard a year or two ago. Nobody showed up then, but maybe they will have later.
There are a few options:
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Conk Fredrick Fleet on the head befrore he gets to the crow’s nest. Let the Titanic hit the berg head-on. Would have lots of injuries but prolly wouldn’t have sunk.
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Bring a pair of binoculars aboard and give them to the lookouts. The ship’s pair had been misplaced.
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Run screaming into the pilot house two minutes before the iceberg was spotted. Two minutes was all they needed to miss the whole damn thing.
You could be thinking of Douglas Adam’s Starship Titanic which came out in 1998.
I remember the computer game- I think it was just called “Titanic.” Wandering around the ship exploring was itself pretty cool. I think I rescued from the wreckage some mediocre paintings by an aspiring artist named Adolf Hitler, and the subsequent publicity averted WWII.
The newest Dr Who has visited the Titanic, not in an episode but mentioned as having happened.
The plot of John Varley’s novel Millenium was that a bunch of future time travelers were gathering people from the past. They wanted people whose disappearance would have no effect on history so they went to go to events like plane crashs and grab all the passengers right before the crash and replace them with life-like dummies. There was a passing reference in the book to them having grabbed the Titanic after it went under water (this was written before the wreck site was discovered).
I remember this game. I never played it but I knew people who did and they found the Hitler paintings as well. (My problem with it was that Hitler, while certainly a better freehand artist than I am or than probably most people are, was no artistic great; his work was Ramada Inn or Starving Artist Sale quality.)
Of course I can’t remember the title OR the author, but I read a time travel novel in which a group of racist, apartheid-loving South Africans opened a time portal to the United States during the Civil War and provided endless supplies, including AK47s, to the Confederate troops. The book was pretty good up until a very, very contrived ending in which the Confederate leadership decided that slavery really wasn’t such a good idea, after all, and the conflict ended amicably. :dubious:
I think the short story would be “Vintage Season” by Lewis Padgett.
That was Guns of the South, by Harry Turtledove. The ending does seem contrived, although you could certainly posit that the Confederacy would have eventually abandoned slavery for economic reasons.
And one shows up(Conservation of Pain) just to save a blues singer from a life of suffering.
Yes, that was it. Agreed, but not in the time frame that the book covered. I loved the part where somebody found the structure containing the secret location of the time portal, and it was full of things they didn’t understand. Strange round objects that glowed by themselves. Glowing screens with associated trays with letters of the alphabet only out of order, so they were dubbed “Qwertys.”
The short story is Vintage Season by C.L. Moore, filmed under the title Timescape.
On preview I see that Baldwin provided a partial answer.