What signals can be probed with an oscilloscope on an Arduino board?
You can use anything that generates changing signal. The easiest source is crystal oscillator (see picture below showing the probe points on Duemilanove). Don't forget to connect your ground. Probing may stop the oscillator, in this case power cycle the board. 

You may want to generate something and see how it looks. For example, follow this tutorial, make a LED fade then connect your scope to the LED and observe how the duty ratio is changing.

In this manner you can see any signal.