Several designs carried a Liberty Head image. Values depend on many factors so it's difficult to pick a single coin as the most valuable.
Among coins normally called Liberty Head dollars, the top regular issue is probably the 1794 "flowing hair" coin. As of 01/2011 its retail value in top condition is about $975,000.
Morgan dollars are sometimes also referred to as Liberty Head pieces, but they're almost universally known by their designer's name instead. The champ there is an 1889-CC coin which retails for about $937,000 in spectacular MS-68 condition.
But of course the most expensive US silver dollar is the fabled 1804 "original" issue, which sells for around $6 million! These coins are unusual in that collectors now know they're not regular-issue dollars and weren't made in 1804. They were actually minted in 1836 in order to create a set of all denominations for presentation to the King of Siam. However they're not considered counterfeits because they were legally authorized by the government and struck at the Philadelphia Mint.
Money can have various values based on condition and certain stamping. An 1885 Morgan Liberty Head silver dollar can be worth between $20 and $400.
Assuming it's a more common Morgan dollar, about $13 for its silver content
$60.00 to $80.00 in circulated condition.
Circulated condition $20.00 to $40.00
Please post a new question after you look at the coin again. A U.S. silver dollar dated 1850 would be of the Seated Liberty series not a Bust type or Liberty head.
There are NO US Liberty Head dollars dated 1846 but there are Seated Liberty dollars dated 1846. Consult a qualified coin dealer
$15.00 to $20.00 in circulated condition.
Assuming the coin is circulated and has no mintmark, the 1881 Morgan (not a Liberty Head) dollar is a very common coin with retail values of $32.00-$39.00 depending on the grade.
The 1984 Liberty Head Silver Dollar was minted in four locations. The CC for Carson City id the most valuable due to the few produced. The degree of wear and whether the coin was circulated affect the value of the coin.
The image on the face of the Morgan Dollar is a rendition of Lady Liberty designed by George T. Morgan.
1880 is a common date Morgan dollar, circulated examples are $17.00-$26.00 depending on grade.
Two different types of silver dollars were struck in 1921 a Morgan Dollar and a Peace Dollar. On the front of the Morgan dollar above Liberty's head is E PLURIBUS UNUM and circulated coins are valued at $15.00-$19.00. The Peace dollar has the word Liberty above her head and circulated coins are valued at $85.00-$185.00