Check above the date with a strong magnifying glass. If there's a faint image of a mint mark you could have a grease-fill error, where bits of crud got into the mint mark recess on a die and prevented it from striking properly. Unfortunately filled-die errors are fairly common so in that case your coin would not be worth more than 50¢ to $1 as a curiosity.
If there is no image at all, I'd have the coin inspected by a professional dealer or grader to see if it's authentic. There have been a few cases of dimes where the mint mark was left off a die, but the only reference I can find is for 1982, not 1984.
A 1978 Kennedy Half Dollar w/no mint mark and even graded at an MS40 only averages $1.00
Without knowing the exact condition i.e. heavily circulated, uncirculated and it's grade, it is impossible to give an exact value. I recently sold a graded 1978 Kennedy Half for $35.00 So if it is one someone gave you as a gift, it could have some value. However if you received it in change, it's value is questionable, and probably worth the $0.50 in change received.
a quarter
Just to make sure take it to a dealer or collector for and opinion, but it's likely from a filled die that caused the mint mark not to strike up.
This date regardless of mint mark is valued for the silver and is worth about $3.25
It's worth 25 cents.
If you got in change spend it, in 1968 the only mint marks used were D & S a coin without a mint mark was struck in Philadelphia.
No mint mark means it was minted in Philadelphia. The quarter is worth exactly 25 cents.
All the Washington Quarters minted in the year 1989 carried a mint mark: "P," "S," or "D." The P and D minted coins are worth in MS60 condition: 75 cents; the S coin was minted only in proof and its value is: $3.00.
It is worth .25¢ The absence of a mint mark simply means it was minted at Philadelphia.
Not enough info what condition is it in and what mint mark
25 cents.
Melt? $5.80. Depending on mint mark and condition it might be worth more.
No U.S. coins dated 1966 have a mint mark. The '66 quarter is worth 25 cents.