There are a few different types of air purafiers with some significant differences in how they work and how much they cost.
There's the old type of air purafier that has a charcoal filter or something like that. These are going to be the least effective, and in many cases not effective at all.
Then you've got air purafiers with hepa filters. Hepa filters are much more effective filters and this will work much better than something like a charcoal filter. However, you'll have to replace the hepa filter every so often, and they're aren't cheap.
Ionic air purafiers have become popular thanks to the Ionic Breeze. The ability to clean the air is still in question though. And it's possible that over time they may create unhealthy levels of ozone in the air. I think the newer models are addressing this.
Electrostatic air purafiers work kind of like ionic purafiers in that they have no filter. But they don't produce the ozone either, so they may be your best bet (and possibly most expensive).