AnneE, house plants absolutely do their part to make your indoor air healthier to breathe. I've read that indoor air is pretty bad with carpet glue, monitor output, paint fumes, plastic outgassing and the use of cleaning chemicals all wafting around the air. Among other things.
One thing I try to do is air out my home for 20 minutes a day, even just by cracking a window in each area. And I did just pick up some houseplants at Walgreens (2 for $10) to help absorb toxins. I got a spider plant and a corn plant, since those each absorb different toxins.
So getting and caring for your houseplants is a good green goal.