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.
It is worth .25¢ The absence of a mint mark simply means it was minted at Philadelphia.
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.
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.