Shazamify allows you to play your Shazams in Spotify, directly from the browser.
Shazamify add a small Spotify icon to every Shazam track page and allows you to play that track directly in Spotify.
UPDATE 5: I had to publish a new extension as the old one was costantly taken down with no explanation, thanks Google again
UPDATE 4: Since mid 2017 Spotify blocked unauthenticated API calls, unfortunately, because of that, the user scripts are not longer working :(
UPDATE 3: The Chrome Extension was taken down without any notice from the store. Thanks Google, thanks! I am trying to figure out what I can do about it. In the meanwhile you can use the User Script solution. UPDATE 2: The Chrome Extension is back only with a new fancy name (Zamify), thanks coypright! UPDATE: Unfortunately the Chrome Extension was taken down from the store because it used the word Shazam. Anyway the good news is that you can still enjoying it with a manual installation :)