Do home air cleaners work for air pollution (such as car emmisions) as well as dander/pollen/allergens?

I've already read that many popular air purifiers actually emitt a lot of ozone, but for the ones that do not, do they work against city air pollution that comes from industrial work or is it just against organic allergens?

I believe it depends on what brand and which filter you buy. Each one uses a different method of filtration and some have combinations of several methods in the same purifier. Here are three different ones I found (the links are below).

The Sharper Image Hybrid GP Germicidal Air Purifier reduces bacteria, mold spores and viruses in the air, and converts ozone to oxygen.

The Friedrich C-90A Electronic Air Cleaner employs three different levels of allergen and irritant removal and claims to remove tobacco smoke, pollen, and dust.

The AllerAir Air Purifiers help clean the air of particles, gases, odors, smoke, mold, and various pollutants. It claims to be ideal for someone who "wants features commonly ordered for use in hostile or toxic air environments such as medical facilities or government military buildings in order to reduce potent airborne contaminants."