Hearing your own playing is an incredible boon to becoming a good performer. In many ways it will prevent you from becoming a bad one, because you will always hear yourself. My teachers have always asked, "can you hear yourself play?" and I respond "yes" and they say, "that's good, keep it that way."
Sometimes, however, when I play, I will lose sight of how it sounds, especially if I am focused on something technical. To me, how the piano sounds is key, and your technique can improve if the sound improves or vice versa - it depends on where talent lies. If you cannot hear yourself play, I would suggest playing a very slow, simple piece, and focusing on the sound, for practice. Then try applying your concentration to the harder stuff. What the other guys said about recording holds true as well.