Probably every business would love to dominate their product category.
The textbook case is Apple. They so dominate several fields – portable music players, tablet computers, smartphones – that you can’t have an intelligent discussion without reference to iPod, iPad, or iPhone.
How did they get that way (besides the fact that Steve Jobs is a legitimate, screaming genius)?
Here’s an excellent article on the subject:
Notice that in several cases, innovations that Apple is credited with were NOT in fact first introduced by them.