A friend and I were discussing notable people who have no known living descendants. We came up with:
Shakespeare
Lincoln
Washington
Mozart
Beethoven.
Can you name other examples?
Trotting out the Martirologio Romano and the Jesuit Saints counts as cheating?
Some Spanish notables with no known descendants living today:
A bunch of kings (most notably Carlos II, last of our Hapsburg)
Quevedo
Góngora
Lope de Vega
Plenty of Popes. Absolute oodles of ancient historical figures. All major religious figures that I know of.
Several kings and queens of England, including Edward VIII (later the Duke of Windsor), William IV, Anne, Elizabeth I, Mary I, and Edward VI.
Jesus???
I take it you haven’t read The Da Vinci Code?
Laura Ingalls Wilder
As far as I recall, at least…
I came in to mention Laura Ingalls Wilder. Her only daugher’s son was either a late miscarriage, stillborn, or died shortly after birth. None of her sisters had any children either.
Helen Keller.
Emily Dickinson?
Not Muhammed. He has a lot of them. And even though Washington has no living descendants, his wife does.
Marie Antoinette, Queen of France.
Muhammed has known living descendants? How come they don’t make more noise?
Oddles of people are direct familial descendants of Mohammed (PBUH). He did not live that long ago, had lots of wives and lots of children. Further, his linage is quite well-researched.
Well, colour me slightly less ignorant.
Really? I thought I read about one of them in Huckleberry Finn. 
Cleopatra.
Rene Descartes didn’t marry and his one daughter died when she was a child. He left no descendants.
I was just reading Richard Dawkins’ Ancestor’s Tale, and he brings up the concept of a “concestor,” also known as the most recent common ancestor (MRCA).
From this article: “The MRCA of everyone alive today could have co-existed with a large human population, most of whom either have no living descendants today or else are ancestors of a subset of people alive today.”
If you go back further in time, you reach a point in the past where all humans alive at that time either have no living descendents or are common ancestors of all living humans today.
The most recent common ancestor for all humans was surprisingly recent. One estimate from the linked article is a MRCA living in the second or first millennium BC. Another model suggests that the MRCA of Western Europeans lived as recently as AD 1000.
With respect to the OP, eventually every person, including historical figures, either has no living descendents, or becomes an ancestor of everyone alive.
Indeed; I remember reading in a couple of places that someone calculated that the odds are very, very high that everyone in Europe and Asia is a descendant of Mohammed, because of the way the number of all descendants grows with every generation. Because of the same reason, this guy opined that chances are high that everyone in Europe is a descendant of Charlemagne, and that everyone in the world descends from one or more Egyptian Pharaos.
I guess that means he wasn’t forward-thinking?