Are air purifiers/filters actually effective for their given purpose?

I have asthma and allergies, so have been considering buying an Air Purifier to keep dust and pollen to a minimum, if that’s what these things really do.

I’m very skeptical about gimmicky marketing, so before I spend $100—$200 on one of these, please share your experiences on whether they create a noticeable difference on removing dust from the air.