Deckman's hit the nail on the head - all the resonances of our skull bones and sinuses make what we hear quite different to what the audience hears. You get a hint of it with the sean nos singer's trick of pressing hard on the back underside of the ear to close the canal; try it while singing and your voice will sound very different. You may, however, be better able to pitch like that.
The reason we sing better in the bath is that our bathrooms also resonate a lot - all those shiny surfaces and the echoes that scatter and bounce around are very kind to the voice - which is why karaoke machines always have the reverb turned right up.
And the reason why a lot of recordings sound awful is because the microphone doesn't pick up those resonances - all it gets is the flat tone 'straight from the horse's mouth'. You need a recording engineer to add the 'life' to the sound.
None of which helps me - I just hate hearing my own voice, whether I've heard it on dictaphones and on pro studio decks. I'm just glad that other people seem to like it!
And kendall, I can still hear you sing in my head - having heard you in the UK some years back. Like a good wine, that voice keeps well! Thank you.