Here's an article from the EPA about residential air purifiers. They advise as first steps to avoid/remove sources of indoor air pollution and to improve ventilation with clean outdoor air. Once the limits of these techniques are reached, they advise that air purifiers may be useful, in certain circumstances. A telling quote:
How effectively air-cleaning devices alleviate allergic and other health symptoms remains uncertain. Strong data linking air-cleaning devices to reduced health symptoms do not exist. Many studies have associated air-cleaning devices with reductions in airborne indoor pollutant concentrations, but more clinical studies are needed to determine whether air cleaners significantly affect health outcomes. A literature review documented only a limited number of studies that attempted to evaluate the clinical outcomes of air cleaner use. These studies focused on more sensitive groups, such as asthmatic and allergic individuals, children, and the elderly. A number of the studies had important limitations, such as small study size, short duration, and lack of blinding (i.e., subjects and scientists were aware of air cleaner operation), which may result in a placebo effect. The results were also more suggestive than conclusive.