Well there are rare as in hard to find and those that are stoppers, ones that require substantial patience and deep pockets to acquire. I will assume that you mean those that are hardest to find but still available to the average collector for a premium.
First off are what are called the key date cents, these are generally regarded to be the following:
1909-S
1909-S VDB
1914-D
1931-S
All of these coins carry moderate to large price tags depending upon grade and are very unlikely to be found searching through bags of old coins having been pulled from circulation for the better part of a century.
Next are the semi-key dates. This is less agreed upon than the key dates. With some people calling anything with a low mintage a semi-key date. I will use a more traditional listing that has fewer coins. They are as follows:
1910-S
1911-S
1912-S
1913-S
1914-S
1915-S
1922-D
1924-D
In addition the following cents are hard to find but haven't traditionally been considered semi-key but still may be refereed as such by some sellers especially on Ebay.
1909-VDB
1922-D weak D
1923-S
1926-S
1931-D
Then there are those cents which are not needed to complete a regular set of Lincoln Cents as they are mint errors. These are also some of the most expensive coins in the entire series running thousands of dollars or more for a nice example. They are:
1917 Double Die Obverse
1922-D No D plain strong reverse
1955 Double Die Obverse
In terms of pure rarity these are far rarer than even the key date Lincoln Cents but are not collected as coins representing a date/mintmark but rather as rare errors.
Those are just a few of the many different collectible mint errors in the series, a complete list would be perhaps a hundred different coins.
1909 S VDB wheat cent is a rare date.
Neither of these are considered rare.
$35,000.00 to $81,000.00
The most valuable ones are the 1943 copper penny, and the even more rare 1944 steel penny.
It's worth about 3 cents. Post-WWII wheat cents aren't rare or valuable.
If your asking can you find a 1916d in change, it's rare but yes.
This is considered an "error coin" and is rare. Depending on the "eye appeal", rarity and significance of the error, the penny may be moderately valuable.
Yes. Wheat pennies were made 1909-1958. A wheat penny has wheat on the backside.
3-10 cents, depending on condition. It's not a rare coin.
That depends on the date. Come back and ask again when you have something specific.
2 to 5 cents in circulated grades. This is not a rare coin.
3 to 7 cents in circulated grades. This is not a rare coin.