How much are we talking about here?
As much or more than that from car exhausts,gas cookers and open fires?
Less than you get if you drink apple juice, orange juice, wine, brandy or many other drinks. Of the things you'd probably prefer not to ingest, formaldehyde is also present (I believe) in shampoos, bubble bath, deodorants, mouth wash and other "hygiene" products.
Aspartame is broken down by the body into a small number of chemicals, one of which is methanol. The body handles methanol by processing it into formaldehyde and then into formic acid. Both formaldehyde and formic acid are very poisonous and will cause death in sufficient concentration, but a healthy body can deal with them at very low levels.
Methanol is also present in the juice of fruit high in pectin and citrus fruits and, unless it's specifically been removed, in many products made from them. I think it's also a breakdown product of some drugs. Apple juice is, as far as I recall, anything from 0.1% to 1% methanol depending on how the juice is extracted. It's processed exactly the same way (ie. to formaldehyde and thence formic acid) in the body.
The most recent research I could find when I looked (a couple of years ago) suggested that the levels of formaldehyde produced in the body as a result of the consumption of what might be considered "normal" levels of aspartame are not significant when compared with the levels present as a result of normal activity.
(I admit it's a struggle to find this stuff out though -- there's an awful lot of discredited research, PR and unreviewed work out there, on both sides of the argument. Neither am I a biochemist. When we reached the point where we were considering that it might be acceptable for our children to have drinks that might contain aspartame, I just felt that I should try to get a proper understanding of the issue rather than blindly accept what the scare-mongers and conspiracy theorists would have us believe.)
James