What is the value of a 1942 US nickel?

There are four varieties of nickel dated 1942, made from two different metals.

5¢ pieces were made of the standard 25% nickel / 75% copper alloy until mid-1942. These coins were struck at Philadelphia and Denver. The D mint mark is to the right of Monticello.

From mid-1942 to 1945 5¢ coins were struck in an alloy of copper, silver, and manganese in order to free up supplies of nickel for the war effort. These "war nickels" were distinguished by having a large mint mark above Monticello. They were the first coins to use a "P" mint mark to designate the Philadelphia mint.

Look on the back of the coin to see if there's a small mint mark letter. It may be blank, or there may be a P, D or S.

Numismedia lists the following approximate retail values as of 09/2011:

No mint mark (Philadelphia), copper-nickel:

Very worn condition - $0.06

Moderately worn - $0.14

Slightly worn - $0.20

Almost no wear - $1

Uncirculated - $2.40 to $136.50 depending on quality

"P" mint mark (Philadelphia), silver alloy:

Very worn condition - $2.40

Moderately worn - $2.64

Slightly worn - $2.76

Almost no wear - $3.20

Uncirculated - $5.40 to $2220.00

"D" mint mark (Denver), copper-nickel:

Very worn condition - $0.18

Moderately worn - $0.42

Slightly worn - $1.20

Almost no wear - $6

Uncirculated - $17.25 to $227.50

"S" mint mark (San Francisco) - silver alloy:

Very worn - $2.40

Moderately worn - $2.64

Slightly worn - $2.76

Almost no wear - $3.20

Uncirculated - $4.20 to $2060.00
That depends on if it's a regular nickel or a silver "war" nickle. A regular one is worth about 10 cents, while a war nickel is worth nearly $2. War nickels have an extra-large mint mark on them, right above Monticello.
That depends. Some '42 nickels contain silver and are worth around $1.50 in average condition. The non-silver ones aren't worth much more than face value. The way to tell is that the silver war nickels have a large mint mark on the reverse (tails) side above Monticello, and the regular ones don't.
A 1942 S nickel is worth $1.25 in G-4, $1.50 in F-12, $3.00 in EF-40, $10.00 in MS-60.