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Anything that is very cheap and adundant in quantity; something easily acquired.
It's said that in the year 1796, the first U.S. dimes were produced for circulation. Hence, it would make sense for this phrase to orginate sometime after. This phrase looks as though it originated from sometime in the 1800s where a number of different foods were being sold for the the literal price of a dime a dozen. For instance, copious newspapers from that time advertised how certain kinds of food, like eggs, oranges, and peaches, were available for purchase by the dozen, and their cost was nothing more than a single dime. An example of this comes from the Galveston Daily News, 1866:

"The San Antonio Ledger says the city is well stocked with peaches at a dime a dozen."

The earliest I could find of this idiom being used with its figurative meaning of "something that's very common" was in the early-ish 20th century. For example, The Northern Miner newspaper, 1931, wrote:

"'Carners,' the old-timer said, 'is just an overgrown clown. As for the others--Schaof, Baer, Paulino,
  Risko, Campolo--they're nothing but 'dime a dozen fighters.' "

Another example is from the Sandusky Register, 1937, which uses this expression in a figurative sense:

"Smiles were a dime a dozen in the Yankee clubhouse. Even Colonel Ruppert, owner of the club,
was so stated he went from player to player shaking hands."

Reference: newspaperarchive had the newspapers with the idiom quoted above.
* Hugs were a dim
Note: Tracking the origins of popular sayings is tough stuff! Usually, you can find these idioms written down in old books, poems, or newspapers. However, keep in mind that just because they are found from these sources doesn't necessarily mean that they orginated from there. Typically, the origins will be even older than these recordings, but they will still be quoted to give you an idea on how long a phrase has been in use.

Also of note: the origins of an idiom are not always clear, and in these cases, the popular theories surrounding them will be provided. Sometimes, even I'll throw in a plausible guess as to how it may have formed. At the end of the day, hopefully you, the reader, will have a clearer understanding of the phrase's definition, some interesting info on how the saying possibly originated, and an indication on how far back in history a saying goes.
The meaning of the phrase Dime a Dozen.
Dime a Dozen saying origin.
e a dozen at our family reunion since everyone was so happy to see one another.
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