Well, that's cool, Rob. You found a 1937 Washington quarter at a conservation site in Canada? Amazing.
Your 1937 coin is a common date in the Washer series. Most all of the dates and mint marks carry the same value as Rob's, as discussed below. There are a few exceptions that are more valuable than Rob's, and those, too, are listed below.
At a minimum, a pre-1965 Washington quarter is worth junk silver value. Read about this at this CoinQuest link. A pre-1965 Washington quarter contains 0.181 troy ounces of silver. Multiply this by the current 'spot' price of silver (available at kitco.com) and you get the minimum value of your coin. For instance, if silver is, say, $20 per troy ounce, a single Washington quarter dated before 1965 is worth 20 x 0.181 = $3.62 Not bad, especially if you have a bunch of them. Be sure to look up the current price of silver. It changes every day.
Quarters dated 1965 and after are not made of silver and are worth only face value: 25 US cents.
If you want to go into more detail, the first job is to check for a mint mark. If one is there, you will find it under the wreath on the reverse, the 'tails' side of the coin. You may find a D or an S, or no mint mark at all. The coin in our picture has a tiny S mint mark just above the R in QUARTER on the eagle side.
Here are some prices in US dollars for common-date Washington quarters with and without mint marks. The values apply to just about every coin in the series
WASHINGTON QUARTERS DATED BEFORE 1965:
No mint mark: F12: $8, MS63: $12
D mint mark: F12: $8, MS63: $25
S mint mark: F12: $8, MS63: $25
The annotations F12 and MS63 above are numismatic (coin collector) grades. You can see that MS63 coins are far more valuable than F12 coins.
Look at the coins in the picture. The lower coin holds a numismatic grade of Fine 12, or F12. The upper coin grades Mint State 63, or MS63. This gives you some idea about how to grade Washington quarters.
Note also that the MS63 displays a nice luster, or creaminess, or frostiness, and does not look polished or shiny. The presence or absence of luster is a sure-fire method for determining if a coin is uncirculated (i.e., in mint state, MS, condition) or not. Frosty luster is the first thing to leave a coin as soon as it enters circulation.
To estimate the value of your coin, estimate where it falls between F12 and MS63, then use the data to interpolate an approximate value. If your coin has scratches, stains, spots, or has been cleaned or polished, the value goes down, WAY down.
NEVER CLEAN A COIN. CLEANING RUINS VALUE.
A few pre-1940 dates and mint marks are extra valuable. Those with extra value are:
1932D -- $100 in F12, $2000 in MS63
1932S -- $80 in F12, $1200 in MS63
1934D -- $8 in F12, $340 in MS63
1935D -- $8 in F12, $275 in MS63
1936D -- $12 in F12, $800 in MS63
1936S -- $8 in F12, $140 in MS63
1938S -- $8 in F12, $140 in MS63
1939S -- $8 in F12, $140 in MS63
1940D -- $8 in F12, $165 in MS63
Finally, the 1976 drummer version carries no premium. It is worth face value.