Well, there was the guy, I believe his name is Spurlock, who yesterday became the first, and therefore the only, player to ever run a kick back for a touchdown for the Tampa Buccaneers in their entire 31 year existence…
I think you could reasonably subdivide these. Pauling won in two catagories with no sharing, while Curie won in two separate sciences. (and her husband, and her daughter and her son in law also won Nobels, as I recall - must have put some serious pressure on the grandkids). That probably be most Nobels for a family too.
Johnny Vander Meer is the only pitcher to throw two consecutive no hitters.
Fernando Tatis is the only batter to ever hit 2 grand slams in the same inning off the same pitcher.
Bill Mueller is the only batter to hit 2 grand slams in the same game from opposite sides of the plate.
(And you can forget about any one else ever duplicated this feats. Won’t happen!)
Not sure about the time of day, but I do know someone born on that day.
I know; my point was that what the OP was looking for examples of seemed large enough to cover everything.
Consider the question “What things have only been done by the fewest (non-zero number of) people ever?” from the OP. What does that mean?
My parents were the only people to have a child with genetic code as follows: [specs left out for space]
Samuel Beckett is the only person to have won a Nobel prize and to have an entry in Wisden, the cricketing bible. He played a couple of first class (trans: top level) games for Dublin university.
wiki link
Cal Hubbard is the only person who is a member of the Baseball Hall of Fame and the Football Hall of Fame. (Isn’t it interesting how so many of the examples given here revolve around baseball?)
Zev Steinhardt
There was only one Emperor of France.
It’s the nature of sports records. Only one person won the most games. Only one person threw the most touchdowns. Only one person ran the fastest mile. Etc. etc. etc. (Excluding the odd cases where there are ties.)
How do you figure? Even discounting Charlemagne, there were at least three Bonapartes. 
Jeannette Rankin was the only member of Congress to vote against entering both World War I and World War II.
Only one number has been retired by the NHL in its 90 year history: Wayne Gretzky’s number 99.
That’s my point. If you narrow it down enough, your likely to be able to get just one answer. You know someone born on the same day, but what about the same hour? Minute? Second? 10th of a second?
It like these stupid “statisics” that I’ve been hearing football anouncers making.
“Wow, that’s only the second time in history that someone who’s last name was more tha 6 characters long has run for more than 100 yds during a playoff game in an indoor stadium when there was more then 60,000 people in attendance during a waxing moon!”
Gerald Ford is the only non-elected President to survive TWO assassin attempts in 17 days, both made by a woman who had previously made infamous news stories involving crimes against famous people (let’s see anybody break that one).
Damn that was going to be mine! 1900 times the course has been attempted, but only twice has anyone achived TOTAL VICTORY!
(I love Ninja Warrior 
)
This thread is a good read.
I think I am the only person to beat up a ninja AND a pirate!
5-year-olds during Halloween would hardly be considered a great achievement. 
Woodrow Wilson was the only president to hold a PhD.
William Jefferson Clinton was the first president born after WWII.
Nancy Pelosi is the first female speaker of the House
You can narrow this down to the point of absurdity:
Only one person has ever installed a laminate floor in my family room.
Only one person has ever been the fourth president of the United States.