Bissell and Dirt Devil do good in the low tier. (Under $50-$60)
Hoover and Eureka battle it out for middle range. ($80-$120)
For most people that believe more money gets them a better vac - Shark is slowly stealing the spotlight from Dyson but both sell reasonably well for high end vacs. ($150-$200+)
Sebo and Miele still do good for premium price vacuums that sell at or above Dyson's MSRP. ($400-600+)
Kirby and Rainbow are still surviving too - but those tend to be bought measured in decades and not years - they are more of vacuums for a niche market today. Most people that own them are collectors - or have been lifelong users and stick to their guns.
That's just my opinion on how the USA vacuum market goes.