How to show Ethernet status in the OS X menubar

Try MenuMeters (free, has been around forever, and it has an option for Ethernet status, RAM, CPU and disk, you can turn on those that you want) or iStat Menus (newer and fancier, but shareware).

With Menu Meters, if the connection is inactive the (Ethernet) arrows would be gray, otherwise they are red and green. You can change the colors or the arrows for graph and/or throughput. Note however that if the Ethernet is disconnected, but the WiFi is connected, it would still show red and green arrows, because there is an active connection.

Edit (2016): The original MenuMeters is not compatible with OS X 10.11 (El Capitan), however this version works just fine.

There is another app on Mac App Store that shows the status of Ethernet Connection: Ethernet Status

I like it because it is a no-frills app and uses very less space on the menu bar and it also shows status of Thunderbolt network adaptors, so works with my Mac Book Air. Sadly it is not free.