You could make a [tweet a watt][1]. 

There are a couple of alternatives that you may not have thought about:

 - If the washer has an LED you can monitor that,
 - you could use a clamp on current sensor - as discussed on the [Raspberry Pi forums][2] 
 - You could attach a piezo disk/vibration sensor, or 
 - simplest of all set the Pi up as a timer that you set when starting the washer.


  [1]: https://learn.adafruit.com/tweet-a-watt/
  [2]: http://www.raspberrypi.org/forums/viewtopic.php?f=37&t=85260