This tutorial describes in detail how to use the free SensorMonkey service to push real-time sensor data from an Arduino to a webpage for visualization using Processing.js. No server-side coding or Ethernet shield is required. A standard, run of the mill Arduino will work perfectly. You'll also need a sensor to sample some values. I use an accelerometer, but anything will work (a potentiometer, a gyroscope, a tilt sensor, a temperature sensor, a light sensor etc.). If you don't have a sensor, it's still possible to follow the tutorial by sampling the floating input voltages on the Arduino's analog pins as a (somewhat) crude substitute.
After configuring the Arduino to sample sensor values, I use SensorMonkey to publish the data live over the Internet in real-time (Disclosure: I co-founded the company developing SensorMonkey). Using SensorMonkey, I can access the data from any device connected to the Internet and use it to drive a real-time webpage. Proxies, firewalls and NATs can all be traversed. Best of all, it works with standard Arduino boards (Unos, Duemilanoves etc.) and does not require an Ethernet shield. Instead, I use free software called Bloom to network-enable the Arduino and connect it to SensorMonkey. In this tutorial, I visualize the data using Processing.js.
UPDATE 26-06-2012: Non-Windows Users
As an alternative to Bloom for non-Windows users, I have uploaded a Processing sketch, named SensorMonkeySerialNet, to our GitHub account. This sketch is a serial-to-network proxy that also serves Flash Socket Policy files inline. It can be used instead of Bloom in Step 3 for users running Mac OS or Linux.