Asexuality
Asexuality is a term for people who do not experience sexual attraction.
Scientific basis
Little research has been done into asexuality, but a UK survey of sexuality indicated that 1% of adults had never felt sexually attracted to anyone at all. (PubMed) A study of rams (referenced here) also concluded that 2% to 3% of the rams were asexual.
Proposed Models and Definitions
Being such a new and unexplored concept, the definition and categorization of asexuality has been the subject of much debate, not least among asexuals themselves. It is often conceived of as one of four or more orientations (homosexual, heterosexual, bisexual/pansexual, asexual), but is also spoken of as one of two (sexual and asexual) with gender preference being measured along a different axis. (Relevant thread)
In addition, a number of other definitions and more complex models have been proposed: