This type of error is called 'Off Center'. The more of the impression missing, the more it is valued, but those with a readable date and mint mark are the most valuable. If your penny (with no date) is an Indian Head penny it is worth $55.00. If it is a steel penny it is worth $45.00. Wheat pennies and Lincoln Memorial pennies are only worth $3.50.
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1 US cent has the same value the world over! i.e. 1 US cent
The US has minted 1¢ coins since 1793, and at 3 different mints so there are many hundreds of different possibilities. Please post a new, separate question with the coin's date. Alternately, look for questions phrased "What is the value of a <date> US cent?", e.g. "What is the value of a 1927 US cent?" Nearly every date has been asked about and answered.
It's worth exactly one cent.
As at 18Feb09 one US Cent was worth about half an Indian rupee, one US Dollar being worth INR49.80.
The value of any coin depends on its condition and date. The lack of a mintmark simply means it was minted in Philadelphia; US cents, often mistakenly called "pennies" after their British counterparts, have never had a Philadelphia mint mark applied to them.