Three-Legged Cattle
In the realm of animal oddities, it is rare for an animal to be born with three legs. Many animals lose a leg due to injury, but to be born with a non-symmetrical congenital defect is unusual. Missing limbs are not included in the long list of congenital defects known to occur in cattle, suggesting that it is an infrequent event and may not be genetically based.
However, this defect has been documented to occur multiple times. The internet does provide several vintage examples from across the years, most with a similar conformation—a completely missing front leg. Still, the other three legs are entirely normal.
The photograph shown was taken in Poland by Herbert Photos Inc. The calf depicted was reportedly born near the city of Lodz.

The image shown below dates from 1906. Thecalf shown had a twin that had four legs but was blind

This three legged full-grown bull is somewhat more unusual, and is missing a rear leg. It appears on a photo-postcard dating from around 1923.

Other reported cases:
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Three-legged calf (undated)--missing hind right leg
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Vermont postcard (1910)--missing front left
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Thirteen-month-old three-legged calf (Canada, 1925)--missing left front limb.
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Farmer gambles on three-legged calf (United States, 2004)--partial hind limb.
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Three legs don’t stop local calf (2006)--front left
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Tripod (2009)--front left
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Three-legged calf becomes family pet (Ireland, 2011)--missing front limb.
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Unidentified (2011)--front right
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Three-legged calf born in Armavir region of Armenia (Armenia, 2011)--front right.
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Gowri (India, 2013)--left front
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Hopalong (United States, 2013)--right front
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Cow with left hind leg missing due to injury (2013)
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Trinity - left front (2017)
Possible Causes
It is interesting to note that of the cases collected here, 12/16 are missing a front limb. And some of those with missing hind legs are known to have lost the leg due to injury, not as a congenital deficit present at birth. There even seems to be a bias towards the left front limb being missing.
The causes of cattle born with underdeveloped or missing limbs are rarely discussed. The main options are a genetic abnormality or an injury, cutting off the blood supply to the limb in utero. This defect and others may be more common in twin births.
Other cases are less mysterious and occur after amputation.