They make new ones every day so to get a good start buy a copy of Red book an add up all the mintage's That well give you some idea.
That depends on which rare coin you have. Some rare coins are worth only 150 dollars in average circulated condition while others are worth thousands of dollars. To get a more specific answer include the date and denomination of your coin.
None of the US coins dated 1977 are rare.
You need to be more specific, The US has made MANY silver coins of different denominations from 1794 to 2011.
No simple answer, many US silver dollars are considered rare for different reasons, be more specific and post new question.
No coins in 1949 are rare, but as with all US coins, high grade Mint State examples can be valuable.
There is one US coin picturing Harrison and that is the one-dollar coin issued in 2012. They are still legal tender and are not rare.
See the related link below for a price guide to US coins. It doesn't point out the rare coins but you can pick these out yourself. Obviously rare coins are worth much more. Coins with a much higher value than others in that category are probably rare or semi-rare.
Ancient roman coins can vary widely in value, from US$2 or US$3 for a circulated common copper to tens (or even hundreds) of thousands of dollars for very rare uncirculated gold or silver coins.
2011 Lincoln cents are not rare. It just takes some time for "current year issue" coins to make their way into circulation.
Yes. The U.S. has struck many Olympic coins.
Depends on the coins: US Coins: 50 Pennies 50 Dimes 40 Quarters 20 Nickels 25 Dollars
The composition of all US coins including errors is a well known fact, based on the dates and denominations of the coins.