Unhealthy seedlings may be victims of insects. Common insect problems include whiteflies, aphids, and mites. Don’t ask us where they come from, but somehow pest insects are able to show up in the darndest places. All of these insects can be easily controlled with a foliar spray of insecticidal soap, such as Safer's soap. Apply the spray to the undersides of leaves, and reapply it 3 to 5 days later to be sure of getting all the pests. In the meantime, you need to figure out why your seedlings were stressed and make whatever changes you need to make to get them back on the route toward healthy growth.
Few diseases bother seedlings unless you use soil from the outside garden. Damping-off, a fairly common fungal disease that leaves plants lying dead in their pots, occurs when the seedlings are allowed to stay in a damp condition for too long. To avoid the disease, use a sterile soil mix and water only in the morning, before noon. To provide adequate ventilation for the plants, you may need to set up a small fan. This is a good step to take if your seedlings are growing in the basement where air flow may not be very great.