Look up the sexual identity of asexuality. I'm an asexual and I feel no sexual attraction towards anyone, however I find many men (I'm hetero) to be aesthetically attractive. I enjoy things like holding hands, hugging, and light kissing (not making out). I do not enjoy sex or a whole lot of physical touch otherwise.

Asexuality is a spectrum and people vary from being repulsed by sex to actually not minding it. They vary from hating touch to enjoying cuddling... There are all different types of attraction too, not just sexual attraction. There is aesthetic, sensual, and romantic attraction. Time to do some reading . Here's a good place to start: The Asexual Visibility and Education Network | asexuality.org