The most obvious effect would be that the Xbox never takes off. It would fold like the Dreamcast within a few years, which would also mean no successor to the console.
The Halo series popularized (but didn't invent) a number of concepts and mechanics common in modern FPS games, like regenerating health/shields and auto aim/aim assistance. In addition, it popularized online multiplayer on consoles. The first two mechanics would probably have not been adopted by a lot of future games; on the other hand, I think online multiplayer on consoles was inevitable.