You do NOT need to install a third party app.

Both Google Chrome and Firefox support this functionality. (ok, technically these are third party apps, but lets assume you are not using safari.)

Chrome:

1. Open gmail in chrome.
2. In the address bar next to the "bookmark star" you should see a grey diamond. Click on the diamond
3. Select "use gmail".
4. If you do not see the gray diamond, follow the instructions below.

If you made a mistake and selected "No" and you really wanted to select "Use Gmail"

1. With Chrome open, copy and paste this into your address bar at the top: chrome://settings/handlers
2. Under the Ignored protocol handlers section, Click on X to the right to delete.
3. Close and open Gmail.
4. Answer the question correctly this time. :)

Source: http://productforums.google.com/forum/#!topic/chrome/hnRteY7bHfE

Alternative way, if you need to do this programmatically.

Firefox:

See @Am1rr3zA answer on this question. Click here to jump to his answer.

Safari:

See @fpotter's answer on this question. Click here to jump to his answer.

Is there anyway to make Apple Mail open all links in a browser behind Mail without the need to right click?

Command-click the link (same thing in Safari will open links in a background tab).