Stinkyattic is likely 100% right about the disease and the cure, which is prevention.

To be sure, look at the base of the stem at the soil line. In the first stages of damping off, the stem will look water-soaked and a little narrowed, then it will look pinched and dead and the plant will fall over like a tree when it's cut. Some of the seedlings may not get that bad and may survive, but they will be weakened.

Hygiene is the most important preventive, and stinky gave you some good pointers there, but temperature and moisture control are almost equally important. Damping off fungi thrive in cool temps, high soil moisture, and high humidity. You want to keep the soil somewhere around 80 degrees. Higher isn't bad within reason, but you'll be watering more often.

Also, follow her advice on watering. You don't want the top layer of soil to stay moist all the time, so misting them every day is actually the worst possible way to water them. Wait until they are just barely wilted, or the pot/tray seems lighter than it should when you pick it up, then briefly water from the bottom. You don't want the soil soaking wet, just moist.

Other things you can do if you're anal:

Soak the seeds for ten minutes in a 1:10 solution of household bleach:water, then rinse. This will sterilize the seeds themselves and also speed germination.

Before sowing, dust the seeds with a powdered fungicide, such as Captan, that is labeled for damping off.

Bottom line is that damping off is much easier to prevent than to treat. The only treatment I know of is to drench the soil in a mixture of Captan and water, and that doesn't work well.