There are medical reasons for pickiness too. It is a symptom of some sensory problems, and at that point it is more of an issue of texture than flavor. My nephew had pretty severe problems with it when he was younger, to the point that as a three year old he would starve himself for 3-5 days with
nothing. No amount of punishing, threatening, bribing, etc. ever worked because it wasn't a behavioral issue. Some foods, particularly those with a soft or slimy texture, triggered a gag reflex and he would end up throwing up if they forced him to eat. Some things he would nibble at were quesadillas and string cheese. He would eat eggs our chickens laid, but not store bought ones. I know it must have been a difference in the eggs because he didn't see us prepare them, and had no idea they were different in any way. They were just more palatable for some reason.
Most of my professional experience is in childcare, along with having a toddler of my own. I remember one boy who was three years old, and had a lot of sensory issues. Brilliant kid, some things seriously bothered him. Some days no matter what we served, he wouldn't touch it. Well, it turned out (as he learned to talk we found this out) he has synesthesia. Seeing certain colors while eating changed the flavor on his food. Serving cheese on a green plate made it taste like poop, according to him. So much so, that he wouldn't touch it no matter how hungry he was. But then, anything served on a hot pink plate tasted amazing. Once we figured it out, it was easy to adjust.
Here's a pretty good link about sensory integration disorders with articles on food aversion:
http://www.comeunity.com/disability/sensory_integration/index.html
With most kids, having them help plan meals and pick things out at the grocery store goes a long way. I ask my two year old what fruit and vegetables we should get, and she helps me pick out the apples, oranges, broccoli, etc. that she thinks look good. Then she's excited to eat the food she has picked out once we get home.
If you can give them little "jobs" in meal preparation, that is helpful too. Like, if you're slicing carrots, give a toddler a plastic knife and a carrot to saw at.
My daughter used to despise anything green. When she was one and a half, I got my seed catalogs in the mail, and we would sit together and look through them. I'd point out all the beautiful flowers, tell her their names, go through all the vegetables, name them all. She learned a lot, and I started asking her what kinds of vegetables and flowers we should grow.
She picked what to put in the garden. She "helped" us plant it (mostly made mud pies) and was very excited to eat the plants when they grew. Every day all summer long she went outside and pulled a leaf off the kale and ate it. She started asking for kale with her breakfast, etc. Even if people don't have land for a garden, they can have their child pick out some lettuce or carrots and plant them in a little window box, or container on the patio.