I include Miller here less for his art (which is good) than for his exceptional storytelling ability. The comics he created in the mid-80's, sometimes with David Mazzucchelli as a collaborator, are amazing in their use of the comics medium, and should be studied by anyone who wants to create dramatic comics. I like how he very deliberately varies panel sizes to create a rhythm, the staging and sense of design in crafting both single panels and entire pages, the ways he juxtaposes panels to show flashbacks or different aspects of a story, and how he will often convey information and create a mood by drawing silent, expressive faces.
Unfortunately, after the 80's, Miller's writing quality declined steeply, and I would recommend against buying anything he's written since the first Sin City collection, from 1991.
Two of Frank Miller's main inspirations are Goseki Kojima and Will Eisner.