Now when I say leggy, I don't mean a great pair of gams. Leggy, as in leggy plants, means the stems of the plants become very thin and tall. Seeds are packed only with enough energy to germinate. Once the seed heads begin to poke out of the soil, the seed has pretty much used up it's energy stores and begins looking for light to provide the much needed energy. Developing seedlings require a lot of energy which means a lot of light.
Growing seedlings actually require a bit more light than comes through most south or east facing windows. Many hardcore gardeners (you know, the ones with leather jackets that keep gardening spades in the pockets...hehe) use complex set-ups and systems for providing light. But...folks like myself who are just starting out or can't afford such things, there's still hope for those spindly little suckers.
Brassicas like broccoli, cauliflower, brussels sprouts, and cabbage tend to be more prone to legginess. I'm not sure why, but it's true.
What can you do about legginess?
Provide more light. This is the root of the problem and this should be addressed above all else. You can use the windows, but when you can try to use greenhouses, cold frames, etc. Even if you can only get them out now and then it will help! I put mine out today during some decent weather and though they weren't fixed in an hour, they definitely seemed to perk up.
Pot up and/or bury those wimpy stems. If you had room in your pots like I did, you can add more soil to either fill up your pot (if the leaves extend above the pot) or add enough soil to bury the stem up to the first set of leaves. If you don't have room or would prefer to go ahead and move them to a larger container, this will work as well as long as you bury the stems up to the leaves. The stems will put out roots eventually to help anchor the plant.
You can also just bury the stems when you transplant. This is fine too.
Before burying the stem
After burying the stems. (The discolored paper is from the inks in it)