BIRTHDAY CAKE - nearly all commercially baked goods are off limits when you have nut allergies. However, Pepperidge Farm frozen cakes are presently NUT-FREE and not made on a shared mfg line. Available at your grocery freezer, they thaw in 20-60 mins... on the drive to the birthday party! Of course, we still must make sure the hands and eating surfaces are washed down.
PIZZA PARTY - most deluxe pizza places make something with pesto in their ovens. That makes most pizza off limits. What to do when your kid is going to a party where everyone is eating pizza? I call Papa John's. As a backup, I call Dominos - their facilities are usually NUT-FREE. I call one close to the party location, confirm they aren't baking any promo items with nuts or other ingredients that could be contaminated with nut dust, place an order for delivery to the party address and let the host know. If Dominos is not able to say their ovens are nut-safe because of fancier promotional fare, then I bring a mostly baked frozen pizza from home and finish it off in a microwave at the location (usually employees have a microwave they use). Again, we still make sure the hands and eating surfaces (and employee microwave) are washed down. I always travel with wipes and use soap and water where we land.
CRACKERS, CHIPS, PRETZELS, CEAREALS - what I can say here is that Snyders' products are NOT SAFE. However, most made for kids brands (e.g. Gerber) are nut-free. Ritz Crackers, Pirate's Booty, Back to Nature Apple Blueberry Granola are presently nut-free.
***Organic does not mean safe. Annie's brand is not nut-free. Amy's brand is generally not nut-free. Barbara's brand is not safe from tree nuts.
CANDY - this is a real danger zone for nut allergy sufferers. There's Vermont Nut Free Candies, but also, from most grocery or drug store candy aisles: Dum Dum Lollipops, Skittles, Lifesaver Gummies (not Gummy Bears!), Sweet Tarts, Trader Joe's Fruit Leathers are NUT-FREE. Chocolates, in general, are off limits because they are made on the same equipment as nut-containing foods.
ICE CREAM - another danger zone for nut allergy sufferers. Most frozen treat makers have a flavor with nuts in it that is made on the same line as the flavors/items without nuts. Even italian ice mfrs use nuts. I have found Breyers Vanilla is essentially NUT-FREE. Unilever told me that they break down their equipment and thoroughly wash and test it for traces of nuts between batches. That's as safe as I have found, in the mainstream, and its a big company that cannot afford to be sued for false labeling. Their labels do not include nuts in their allergy statement, thereby representing through silence that there are not traces of nuts in their vanilla ice cream or frozen yogurt. Also, Annette's Homemade Italian Ice (Armitage@Bissell) can dish up NUT-FREE, no cross-contamination servings. They have several regular customers with nut allergies and segregate their safe italian ices in a separate freezer, and use scoops that are specially identified for the non-nut containers.