The original answer was written for Ubuntu 11.10 & 12.04.
Since then, the indicator interface was changed for 12.10 & 13.04. However, the maintainer has not released a version since then for later Ubuntu versions. No code commits in the launchpad PPA has been made since first quarter 2013.
Thus I have forked the project, fixed a few bugs and made it available for 14.04 Trusty users. Feel free to check out the code on GitHub and help out with the maintenance.
internet up

internet down

how to for 14.04
It requires an indicator from my PPA together with a custom ping test script:
sudo add-apt-repository ppa:fossfreedom/indicator-sysmonitor
sudo apt-get update
sudo apt-get install indicator-sysmonitor
mkdir -p ~/scripts && cd ~/scripts
using:
gedit pingtest.sh
Copy and paste the code below into the new file and save & close.
Give the file execute permission:
chmod +x pingtest.sh
Start the indicator
indicator-sysmonitor &
Then in the indicator-preferences click New:

Then enter the details as shown:

i.e. use the command
$HOME/scripts/pingtest.sh
Click OK, followed by the following actions 1,2,3 & 4:
code
#!/bin/bash
if ping -c 1 -W 2 google.com > /dev/null; then
echo "Up"
else
echo "Down"
fi