I have just come across this fantastic resource which will help you to learn piano by ear.
The utility takes you from absolute beginner piano level through to a really high level and trains you to recognize the intervals between notes. The theory is that once you have learned to recognize all of the intervals then you will be able to play any song by ear with out needing to see the music. There are full instructions on the site but for me I spent hours just playing around with the utility. It made me remember my time at the conservatory.
Have fun with this and see if you can learn piano by ear yourself.