I think in images, spacial relationships, shapes. Some people, when I mention this to them, shrug as if I'd said something as obvious as 'the sky is blue'. Others look at me like I'm speaking gibberish, because what I'm saying makes no sense at all. What I find most interesting about all of this is how such little effect this seems to have on how we as a group see the world overall.
I am one such "auditory thinker". Despite learning to read music from a young age and a lot of practice, I have never been able to sight-read music. I do however have a good auditory memory and I have always been good at playing music from memory, even compared to other musicians.
Perhaps counter-intuitively most classical musicians are "visual thinkers" and are very good at sight-reading and less good at playing by ear.