I always thought plants were cool. Though I also grew up with plants. It's funny, even today the smell of marigold, petunia, and tomato seedlings bring back childhood memories. Of course very few people will be exposed to the vast array and quantity of plants if they don't "live" in a nursery. But there are some nice little things you can do in your house to introduce your kids to plants.
As we all know, kids have a rather short attention span. Picking a plant that takes 3-4 months to germinate is probably not the wisest thing to use as an introduction for kids. So the first rule is to try and select plants that have large seeds that germinate quickly. Vegetables work great, though they should be started closer to May. Pumpkins are a real joy since kids always assure you they will have the biggest pumpkin in history, even if you planted a pie-pumpkin. I also like tomatoes since they grow quickly, string beans which are really easy as well. Peas are nice, but you need to watch for birds. Sunflowers are another easy one and you can get them in little "dixie-cup" kits that makes it more interesting for kids. Nasturtiums are nice too since they're big seeds and grow quite easily.
Another nice little indoor project is Mung Beans or bean-sprouts. They're a little different to grow, but it's great when your kids can take part in a plant-project where you can eat the results. All you need is a jar, some water, some seeds, and a little cheesecloth. Put the seeds in the jar with some water and seal the top with the cheesecloth. Rinse the beans and change the water a few times a day and in no time, you have bean sprouts for dinner.
If you have cats, cat grass is another great indoor project for kids. The seed resembles wheat and they germinate quickly. Kids typically love giving their pets treats and growing their own cat grass is a great indoor project.
For a more long-term project, I've seen quite a few kids enjoy growing cacti from seeds. Now this takes patience, but it really is a fun project. At the nursery, we have a large 6' cactus which was given to us. Somebody called us and he started this cactus from a small 1 1/2'" pot and had it for most of his life. He moved once and cut it down with a chainsaw, but it regrew. When he called us, it was simply too big for him to move again so now it has a home in our nursery.
It's really rewarding when a young person can grow and nurture a plant from seed to maturity. It teaches about life, about nature, and patience. It also shows kids how we must co-exist with Mother Nature.