Our kids really don't have an option - they have to eat what's on their plate. I try to do my best to offer as much variety as possible. I keep the veggies around that I know they like best. My husband hates most vegetables, but even he's agreed to eat them for the sake of our kids.
I've heard of people having a small garden and letting their kids be part of the growing process. Your kids are the same age as mine, and I think they'd really enjoy it.
We've been making a Buffalo Chicken dip lately served with veggies (broccoli, carrots, celery, cucumber, peppers), and they love to "dip" it in there.
Raw veggies have the best nutritional value, but letting the kids help experiment with different recipes may be a good way of getting them involved.
Or, maybe even go to the produce section of the grocery store and ask them to pick something different once/week to try. My son hates canteloupe - even the amazingly succulent ones from the farmer's market.....that may be another great way to get them interested, too. Take them to a local farmer's market and let them explore with some of the offerings.
Good luck!