Allergies and other kinds of substance intolerance are a problem for many people, and can be a real hassle while traveling. However, with proper preparation, one can still enjoy traveling safely.
Being cooped up in an airplane can expose you to allergens while airborne. For example, microscopic nut particles enter the air of an enclosed cabin whenever anyone eats them, and pet dander is carried into planes on other passengers' clothing even when no animals are in the cabin.
If you have food allergies, most airlines will accommodate your dietary restrictions when you book your flight. The choices will vary depending on the airline but typically include vegetarian, religious, dietary and child meals. Typically these meals get distributed first, before the 'main' options. Depending upon your allergies, the normal meal may work for you. Flight attendants for some air carriers have a list of ingredients, or it may be available on their website. Alternatively, you can pack some food with you for the first leg of your trip so you can eat safely on the airplane. This may be the best option for people with severe food allergies, multiple allergies, or unusual allergies. If your destination doesn't allow you to import food, you can always throw away any remaining food just before arrival.
For non-food allergies and other sensitivities, such animals or perfumes, the flight crew may be able to rearrange passengers so that the person allergic to dogs doesn't have to sit next to a service dog.
As a practical matter, airlines can't guarantee an allergen-free flight or prevent other passengers from bringing in allergens. There are few effective ways to mitigate airborne exposure of allergens inside an airplane. Upgrading to a more expensive cabin class (with less dense seating) can reduce the amount of potential exposure from other passengers. Some people with allergies pre-medicate with an anti-allergy drug (such as diphenhydramine, which is often sold under the brand name of Benadryl) to reduce the severity of any problems they might encounter during the flight. Wiping down armrests, tables, and other surfaces may reduce exposure, especially if you have a contact allergy and the plane is not very clean.
Air carriers can require people with allergies to get medical clearance before boarding, just like any other person with a life-threatening medical condition. A letter from your regular healthcare provider that says you are fit to fly and lists any appropriate precautions may be helpful.
Some requests, such as not serving a food that you're allergic to, requires advance notice. You are more likely to find this request granted if you're allergic to peanuts or tree nuts, than if you ask them to stop serving milk on board. In case of a dispute, it may be helpful to have written proof that the airline received your request. The laws vary dramatically between countries. Some are not required to accommodate people with disabilities, or their duties are limited. The airlines generally post information about their policies on their websites. If you are concerned that you may be denied boarding, then consider travel insurance.
For a traveler with allergies, a short train trip between nearby cities might not look very different from an everyday commute. Longer trips, however, benefit from the same type of planning that you would use on a transoceanic flight. However, on a train, if you're sitting near an allergen situation, you can usually get up and move to another part of the train.
If you have food allergies, most longer trains provide some sort of food service, and much of that is pre-packaged and labeled. You can also bring your own food with you.
Always bring your allergy medications. Trains are on the ground, which means that seasonal allergies stick with you.
A frequently used option for people with allergies is to stay in an accommodation which gives full access to a kitchen. This allows travellers to go to local supermarkets and buy what they need in order to be healthy.
On most trips, toiletries and clothes are easy to manage: Bring everything you need from home, so you don't have to use anything that you're uncertain of. If you'll need to wash laundry in another country, consider bringing along your own low-allergen laundry detergent. People with skin sensitivities or contact allergies can pack their own bed sheets and pillowcases as well, so that they can have a layer of "safe" fabric between themselves and the hotel bedding.
If you have potentially severe allergies, you should always carry medical alert information. If you're traveling where people don't speak your native language, then you need that information in the language of your destination. If you're not fluent in the local language, then get your needs in writing, on a card or piece of paper that you can hand to restaurant employees. Don't just write "wheat allergy" or "gluten-free" and leave it at that. If you have a wheat allergy, then write out that you cannot eat anything containing any form of wheat, including ingredients that contain some wheat, such as soy sauce and some sausages.
Always bring your allergy medicine, even if your allergies are seasonal, and it's the wrong season. Do check that your allergy medications are legal at your destination, or that they don't require extra paperwork. For example, diphenhydramine is regulated as a prescription-only medication in Zambia, and Japan permits it only in 10 mg pills (the 25 mg size is more common in much of the world, including the US).