A few things I've found to actually work (sometimes) with kids and good food

*I once read that we all need to be exposed to brand-new flavors something like 21 times before we develop a taste for them. I've been telling my daughter this for years and so she knows that she has to try everything, every time, because one time she just might like it. It's worked as her tastes have changed (and it works for grown-ups, too; note my newly developed taste for sushi at the age of 35. Just in time to get pregnant and not be able to eat it and thus crave it horribly for the next nine months).
*Everyone in our family gets to pick one food that they never, ever have to try. It needs to be permanent; it can't change with every meal. I figure that kids, just like grown-ups, have things they really dislike and that should be respected, to an extent. My daughter's is broccoli, my husband's is grapefruit, and mine is eggs.
*In the obvious but true category: kids are more likely to eat things they pick out and help cook. When my daughter was old enough to read, we found a couple of good kids' cookbooks and we like to have her be primarily responsible for picking meals from them once a week or so. She struggles with math, and so the fact that cooking is a great way to understand fractions better is a great bonus. The cookbook we like the most right now is the DK Children's Cookbook. Another great resource is Family Fun Magazine.
*Take kids shopping with you whenever possible. And yes, I know it's a pain. I know you can get it done faster by yourself. I know sometimes you can tell your husband you are shopping, then get it done quickly and stop for a latte and a brioche and read the paper, while the kids are at home with him. Just take them with you sometimes, especially when you go to the farmer's market. Ask your child to pick one thing they've never eaten (one nutritious thing; not one new flavor of pop tart) and then go home and figure out together how to cook it.
*Garden. This theoretically works; I have a black thumb of death and kill most everything I plant. I do manage to grow tomatoes and rhubarb and zucchini and herbs every year. Let your child plant their own patch and eat what they grown.
*Join a CSA (community supported agriculture-click on the link to find one near you). Getting a mystery box of produce delivered to your house is exciting for kids and grown-ups. It's like a treasure hunt. There might be a plum! There might just be broccoli!

Getting vegetables down the kids

Nine year olds and vegetables. Sigh.

Here's what she'll always eat:
*Artichokes. One of her all-time favorite foods. Picked for birthday meals. Best prices usually at Trader Joe's-I can't stand paying two or three bucks a piece, which is what they will often cost in the grocery stores around here unless they are right in season. She likes them best plain or with ranch; I have to have bearnaise.
*Edamame (you know, raw soybeans in the pod-nice tossed with kosher salt after you've steamed them for 5 minutes). Trader Joe's has great prices-I always have whole and shelled in the freezer.
*Raw peas in the pod. Good deal when you buy the big bag at Costco for $5. Otherwise, usually pretty expensive.
*Raw baby carrots.
*Baked or mashed potatoes.
*Cucumbers
*Raw green beans and (horror of horrors) CANNED green beans. Gotta love that limp goodness.
*Tomatoes. We never get a good tomato harvest as they are always eaten right off the vine. Happy she enjoys them, but it's only good for those few precious tomato months of the year.
*A few leaves of lettuce or baby spinach.
*Raw jicama

Never:
*Broccoli. I've tried selling it as "little trees" a la Enchanted Broccoli Forest to no good. I think it's the absolute least favorite.
*Most cooked veggies, even with cheese sauce.
*Anything pickled.
*Wonderfully crisp, cooked green beans. Heaven forbid.
*Cooked squash, even with butter and brown sugar. This defies all logic, since it is now really more of a dessert than a vegetable.

Themes: crisp, relatively tasteless or sweet: good
cabbagey or cruciferous flavor: bad

So, my goal for the next month is to find a few more vegetables she'll eat. Wish me luck.