My husband should be answering this since he's the junk food junkie lol, but I'll try
For him it's chips and chocolate that are his weakness. He was super bummed to discover a lot of his favourites had dairy in them. Fortunately, it's pretty easy to identify the ones that have them, just check the allergen statement for milk/eggs... obviously anything with cheese is out LOL. Usually the more natural or artisan varieties of chips (Hardbite, Kettle) have a salt 'n vinegar that doesn't use milk.
In the chocolate realm, you can generally find lots of different dark chocolates that are dairy free, but again, just check the allergen statements, particularly if you're allergic to nuts.
Dad's oatmeal chocolate chip cookies (in Canada) are vegan friendly. They're way better than Oreos! ^_^
If you're feeling adventurous, why not try making some of your own "junk" foods? It's way healthier, and way tastier... plus you always know what's in your food. There's tons of awesome recipes online, and I bet you'd be way happier with your own cookies, cupcakes or snack bars than something you buy in a store ^_^ Good luck!