My picky kids absolutely LOVE roasted asparagus, which many other parents seem surprised by, so I guess maybe that's not typical. With my kids I have to keep everything very "pure"-- no sauces, no seasonings other than salt, and nothing mixed together. They love plain salmon, pan-seared in olive oil with just some nice salt on it. The roasted asparagus, also, just has olive oil & salt. They don't even like butter, which astounds me. (But I guess that's a good thing-- they don't know what they're missing!)
They far prefer raw vegetables to cooked (the only cooked they will eat are the asparagus, and broccoli), so I put out a "crudite" plate most nights, with raw carrots, celery, cucumber, bell pepper etc... I add a couple new things every now and then, to stretch their courage & their palates... they just seem a lot more willing to try out the raw form. It's interesting. They would FAR rather eat a raw carrot, than cooked CANDIED carrots (butter & brown sugar). I do think it's a sensory thing. Cooked veggies can look pretty gross, and the texture isn't always nice. I have a texture thing myself, so I know that it can be a real deal-breaker if a texture is not what you want.
All my kids love black olives (ohhh the lovely salt) and pickles (again, the salt). My 6-year-old just started eating sandwiches finally (just meat, cheese & bread-- no mayo or mustard or other dressing) but he likes to put pickles inside... I think we're all just a bunch of salt fiends.