Pigeon droppings can harbor a fungus and cause a lung problem for humans called histoplasmosis, but it usually only affects those who have weakened immune systems. Although there is controversy whether this really is possible. Otherwise, pigeons can sometimes be infested with mites. When pigeons are removed, but their nests are not, the remaining mites might find you to feed on.
Joy is right that exclusion is the most permanent method. There are products, like Nixalite, that are specifically designed for this purpose. If you use your imagination you can create your own exclusion methods. However, fake bird predators, like a
plastic owl, and sound devices do not work. Also, if you can harass the pigeons regularly, they will stop coming round. Pigeons are not a protected species, and can be harassed any time they are causing problems.
Cleaning is cleaning. If you apply bleach like Joy recommends, let it soak a bit, to help kill pathogens. Maybe wear a dust mask to prevent breathing in particles. Here is a good link:
Cleaning & Pigeons
Here are more internet resources:
Internet Center for Wildlife Damage Management
pigeon management
Pigeons and disease
eHow: Cleaning Pigeon Poop