“Why is there an expiration date on sour cream?” is a joke that was popularized by baseball relief pitcher Larry Andersen in 1988. The joke centers on the name “sour cream,” but the word “sour” doesn’t necessarily mean that “sour cream” is already a bad product. The “souring” simply means that certain kinds of lactic acid bacteria have fermented longer.
 
“How can you tell when sour cream has gone bad?” (without the term “expiration date”) has been cited in print since at least 1984.
 
“At the stroke of midnight, Neil wept softly, cradling the sour cream as it expired” is another joke about sour cream.
       
       
Wikipedia: Sour cream
Sour cream is a dairy product rich in fats obtained by fermenting a regular cream by certain kinds of lactic acid bacteria. The bacterial culture, introduced either deliberately or naturally, sours and thickens the cream. Though only mildly sour in taste, the name stems from the production of lactic acid by bacterial fermentation, sometimes referred to as “souring”.
(...) 
Traditional
Sour cream, made out of cream, contains from 12 to 16 percent butterfat (about 14 grams per 4 ounce serving), and gets its characteristic tang from the lactic acid created by the bacteria. Commercially produced sour cream often contains additional thickening agents such as gelatin, rennin, guar and carrageen, as well as acids to artificially sour the product.
 
eHOW
How to Know When Sour Cream Goes Bad
By Patricia Bryant Resnick
eHow Contributing Writer
You might wonder how anything called “sour” cream could go bad. Isn’t it already there? The answer lies in knowing what sour cream actually is. Sour cream is heavy cream that has been cultured by the addition of specific ingredients under specific conditions. This is done to give sour cream its characteristic flavor and consistency. All you need to watch for are changes to that delightful creamy and tangy state.
     
Wikipedia: Larry Anderson
Larry Eugene Andersen (born May 6, 1953 in Portland, Oregon) is a former relief pitcher in Major League Baseball and current color commentator for the Philadelphia Phillies. From 1975 through 1994, Andersen played for the Cleveland Indians (1975-1979), Seattle Mariners (1981-1982), Philadelphia Phillies (1983-1986, 1993-1994), Houston Astros (1986-1990), Boston Red Sox (1990) and San Diego Padres (1991-1992). He batted and threw right-handed.
 
Google News Archive
7 December 1984, St. Petersburg (FL) Evening Independent, pg. 1, col. 1:
How can you tell when sour cream has gone bad?
 
Google News Archive
13 June 1988, Palm Beach (FL) Post, “Astros’ Andersen looking for answers,” pg. 8C, col. 1:
Larry Andersen, relief pitcher of the Houston Astros, is a deep thinker who has been called baseball’s top amateur philosopher. The Houston Chronicle also calls him the team’s designated non-conformist.
 
“He’s pondering questions Plato and Socrates couldn’t possibly have considered,” says the Chronicle. A sampling:
 
. “Why does sour cream have an expiration date?”
 
Google News Archive
19 June 1988, Spartanburg (SC) Herald-Journal, “Quote marks,” pg. D2, col. 4:
Houston pitcher Larry Andersen, whose motto is “You’re only young once but you can be immature forever,” on mysteries of life: “How can you tell when you’re running out of invisible ink? What do they call a coffee break at the Lipton Tea Company? Why does sour cream have an expiration date?”
 
Sports Illustrated
May 01, 1989
Now Some Comic Relief
Franz Lidz
Larry Andersen, the astros’ comic relief man, lopes through the clubhouse wearing a set of jagged false teeth, chino trousers rolled to high-water length and a T-shirt labeled ROSES ARE RED. VIOLETS ARE BLUE, I’M A SCHIZOPHRENIC AND so AM I. The sunflower seeds speckling his face make him look like a beekeeper who has had a bad day at the hives.
 
He spies Yogi Berra talking to another Houston coach and ambushes him in midsentence. “A few things have been eating at me.” says Andersen. “Was Robin Hood’s mother known as Mother Hood? How do you know when you run out of invisible ink? Why does sour cream have an expiration date?”
       
Google Books
September 1989, Baseball Digest, pg. 68, col. 1:
And, “Why does sour cream have an expiration date?”
(Houston relief pitcher Larry Andersen—ed.)
 
4 September 1990, Lexington (KY) Herald-Leader, “Pressure on the fairways, but laughs on practice tee,” pg. C1:
“Why is there an expiration date on sour cream?”
 
Google Books
March 1992, Baseball Digest, pg. 21, col. 2:
Among the humorous questions Andersen has pondered are, “Why does sour cream have an expiration date?”
(Relief pitcher Larry Andersen—ed.)
 
Google Books
Kings of the Hill:
The Irreverent Look at the Men on the Mound
By Nolan Ryan and Mickey Herskowitz
New York, NY: HarperCollins
1992, 1993
Pg. 151:
His specialty is the little teaser that keeps you awake in the middle of the night. For example: Why is there an expiration date on sour cream?
(Larry Anderson—ed.)
     
The Straight Dope
Why is there an expiration date on sour cream?
May 13, 1994
Dear Cecil:
Why is there an expiration date on sour cream?
— Al Malmberg, Colorado Springs, Colorado

Cecil replies:
Al, you nut! I mean, just spelling it out for the benefit of the slow, it’s already sour, right? Unfortunately, as often happens, I’m obliged to spoil your little joke with the facts. Probably you have the idea that they make sour cream by taking ordinary cream and letting it sit out on the window sill for a couple hours. By and by somebody gets a whiff, goes, “Yo, that’s sour! Ship it!” and two days later you’re spreading it on a blintz.
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But bacterial action doesn’t totally stop, and if the sour cream sits around long enough it will eventually become so sour (or moldy) that it’s inedible. The same will happen to virtually any dairy product, since some sour-inducing microorganisms invariably survive pasteurization. Thus the expiration dates.