NASA has actually done some fantastic research on this. There's a book that condenses that information called "How to Grow Fresh Air" (http://www.amazon.com/How-Grow-Fresh-Air-Plants/dp/0140262431); more recently (but the same basic information) there's been a TED talk on the topic: http://www.ted.com/talks/kamal_meattle_on_how_to_grow_your_own_fresh_air.html. I have a lot of these plants. (also, fyi: plants will make your home more humid. that bugs some people, and if you have a LOT of plants (thus a LOT of humidity), can cause problems. so keep an eye out and tweak as necessary.) That wikipedia article someone else linked is pretty rocking, too.
Mechanical air filters- honeywell, etc- are just that, filters. They capture dust (and pollen, and dander), basically, they don't capture specific molecules of formaldehyde, benzenes, etc. Quite good in their own way, but a different mechanism entirely than plants.
"Ionizing" air filters are basically crap. The worst ones ionize-to-the-point-of-ozone-production, which isn't good for you, and the "best" ones are simply ineffective at everything. I'd stay away from anything that claims to be germicidal, simply because I don't need it and think that for me, a reasonably healthy non-immune-impaired person, it would be ridiculous and counterproductive. I need some germs in my life.