I found one significant article in the medical literature related to this topic. The abstract summary follows:

Background: Allergic reactions to food occurring on commercial airlines have not been systematically characterized. Objective: We sought to describe the clinical characteristics of allergic reactions to peanuts on airplanes. Methods: Participants in the National Registry of Peanut and Tree Nut Allergy who indicated an allergic reaction while on a commercial airliner were interviewed by telephone. Results: Sixty-two of 3704 National Registry of Peanut and Tree Nut Allergy participants indicated a reaction on an airplane; 42 of 48 patients or parental surrogates contacted confirmed the reaction began on the airplane (median age of affected subject, 2 years; range, 6 months to 50 years). Of these, 35 reacted to peanuts (4 were uncertain of exposure) and 7 to tree nuts, although 3 of these 7 reacted to substances that may have also contained peanut. Exposures occurred by ingestion (20 subjects), skin contact (8 subjects), and inhalation (14 subjects). Reactions generally occurred within 10 minutes of exposure (32 of 42 subjects), and reaction severity correlated with exposure route (ingestion > inhalation > skin). The causal food was generally served by the airline (37 of 42 subjects). Medications were given in flight to 19 patients (epinephrine to 5) and to an additional 14 at landing/gate return (including epinephrine to 1 and intravenous medication to 2), totaling 79% treated. Flight crews were notified in 33% of reactions. During inhalation reactions as a result of peanut allergy, greater than 25 passengers were estimated to be eating peanuts at the time of the reaction. Initial symptoms generally involved the upper airway, with progression to the skin or further lower respiratory reactions (no gastrointestinal symptoms). Conclusions: Allergic reactions to peanuts and tree nuts caused by accidental ingestion, skin contact, or inhalation occur during commercial flights, but airline personnel are usually not notified. Reactions can be severe, requiring medications, including epinephrine. (J Allergy Clin Immunol 1999;103:186-9.)

In plain English, this study looked at self-reported incidents, which are always potentially subject to bias, although the symptomatology reported was consistent with peanut allergy. The accompanying editorial states:

"Two things are very clear to me as this debate continues to develop: education and preparedness should prevail. As allergy specialists, we need to continue to be strong advocates for our patients with peanut allergy and other significant food allergies. All potential allergen exposures should be anticipated, and a reasonable, practical emergency treatment plan should be written. We need to educate our patients, the airline industry, our medical colleagues, and ourselves about the best approach to this clinical problem. Specifically, the airline industry needs to be better educated about food allergy and to be willing to work with passengers who raise legitimate concerns. Patients with peanut allergy need to be encouraged to continue in their preventative efforts in dealing with their food allergy and to discuss their concerns with the airlines before actually purchasing a ticket. For example, inquiring about specific flights that serve an alternative snack other than peanuts and trying to book early morning flights when the cabins are generally cleaner are two reasonable alternatives passengers have pursued. As mentioned above, injectable epinephrine and airline personnel trained in its proper administration should be routine on all commercial airliners. In the final analysis, more objective data and proper education will help guide us in the ultimate resolution of this important debate and lower the tension in the peanut gallery."

Although I have nut allergies, thankfully I have not had any serious consequences from them. I agree with the other posters who suggest a compromise between airline and passenger would be best, given the circumstances. If you have a known history of severe peanut allergy, it is entirely responsible and appropriate to let the airline know ahead of time.