The information I have (which can be verified on their websites and by calling and speaking with a disability/special services person):
American, US Airways, and United
do not serve "blatant peanuts" (meaning: bags of peanuts, peanut candy, peanut energy bars, etc.) but all of their snack selections for sale and in first-class are "may contain traces". There are usually tree nut mixes sold in the snack packs, but those do not contain actual peanuts. Neither do the tree nuts in first class. However there may be traces and peanut oil.
Delta and Southwest still serve peanuts. If you ask, they won't for your flight if given enough time (meaning, call ahead and get it on your reservation). The planes...for me...still REAK of peanuts and I've seen residue everywhere. I can't fly Southwest anymore...I used to b/c of cheap flights...but then I'd get contact hives or be sniffly the entire time.
I have no idea about Continental or other airlines b/c I just never had the opportunity to fly them.
Sometimes - if you don't get the right answer or get a mixed answer from a CS rep --- CALL BACK --- and speak to someone different or ask for their manager/supervisor. Every airline now has a statement on peanuts...it's there...no guessing or wondering --- the CS rep just has to find it or pass you to someone who does.
REMEMBER: any airline CANNOT make another passenger bring out peanuts...even next to you. They can ask...but they can't force them. You however, can move your seat or ask the other passengers nicely to refrain or get up and snack away down the plane a little bit.
Good luck
Adrienne