Do house plants clean your air?
Verdict: yes, though you'd need a lot (but an achievable amount) of plants.
I saw this hopeful video on 9gag, of researchers studying how well house plants filter out petrol vapour.
Interestingly, most the cleaning is done around the roots of the plants – not the leaves!
I wanted to learn more, and found this Guardian article, which (I think) interviews the same researchers, and the actual research paper.
The researchers "tested commercial green walls measuring 725 by 725 mm, each holding four plants, in sealed 216-liter chambers" and found the "planted walls reduced total VOCs by 42.47% over eight hours" (credo tldr).
Pretty impressive! A caveat of course is the researchers used a lot of plant (~72cm^2 square) for the given volume (~60cm^3 cube). So to have the same effect in a room, you'd need a lot of house plants!
In the Guardian article, researchers recommend using wall mounted plants, to help squish more plants in. Intuitively (looking at the math above), if you cover your whole wall with plants, you'd probably get a noticeable (maybe not ~40%) filtering effect!