This coin is normally called a Liberty nickel.
Numismedia lists the following retail values as of 06/2009:
Very worn condition - $3
Moderately worn - $5
Slightly worn - $11
Almost no wear - $35+
The value of the 1906 V nickel varies greatly depending on the condition of the coin. This nickel can be worth as much as about 4 dollars depending on its definition.
There is no such thing as a 1906 Indian head nickel(*). The first nickel with that design was issued in 1913. The previous design is called a Liberty nickel; you can find a list of prices at the attached link.
In average condition, it's worth about a dollar.
Remember Roman numerals? V stands for 5 (as in 5 cents), not victory. What you have is called a Liberty nickel or sometimes a V nickel. There's more information at the question "What is the value of a 1912 US nickel?"
15x its face value if you can read the date
The value of the 1906 V nickel varies greatly depending on the condition of the coin. This nickel can be worth as much as about 4 dollars depending on its definition.
1906 is a common date for Liberty Head nickels, most circulated coins are valued at $1.00-$3.00
Must be appraised by a professional.
There is no such thing as a 1906 Indian head nickel(*). The first nickel with that design was issued in 1913. The previous design is called a Liberty nickel; you can find a list of prices at the attached link.
Don't assume every old coin is made of silver. Your coin has a V on it because V is the Roman numeral for 5, so you have a nickel, made of plain old nickel and copper. It's most commonly called a Liberty nickel, but sometimes it's referred to as a "V nickel". See the Related Question for more details.
In average condition, it's worth about a dollar.
The Denver mint did not issue any nickels in 1906, only Philadelphia did. A 1906 Philadelphia nickel retails at $3 to $25 depending on condition.
Remember Roman numerals? V stands for 5 (as in 5 cents), not victory. What you have is called a Liberty nickel or sometimes a V nickel. There's more information at the question "What is the value of a 1912 US nickel?"
Additional information is necessary to properly value your rifle. There were two models available in the Winchester Model 1906. One had a straight stock and the other had a pistol grip stock and was called a Model 1906 Expert. Which one do you have? Also, you did not say, if your rifle was partially trimmed in nickel or was fully nickel trimmed?
The only silver nickels ever made were made in 1942-1945. These nickels contain 35% silver. So a 1906 US silver nickel is worth nothing because there is nothing like that. See the related question below for the value of a 1906 US nickel.
15x its face value if you can read the date
About $9.