Hi --
This is a very large topic and I won't try to completely cover all the pests and diseases which can affect and harm tobacco crops. Tobacco breeders have come up with resistant varieties for many of the wilts, viruses, fungi and molds. Similarly, insects which attack tobacco are of such a large number that I will not be able to mention them all here. There are beneficial insects also. I will simply try to cover the more common diseases and insect pests which are seen in tobacco crops. There are many references online by universities and trade-groups which can be found with a simple search.
Tobacco Diseases
Tobacco is subject to many diseases which are in the general categories of viruses, bacteria and fungi/molds.
Tobacco mosaic virus is often stated as a destroyer of tobacco crops. This is the virus most referenced however isn't the only one. Viruses are generally spread by leaf hopping and sucking insects but can be spread by using tools, implements and even hands which have contact with an infected plant and are then used to touch a plant which is unaffected. While there are chemicals which can reduce or minimize the damage of a virus in your field, for the home grower the best thing to do when an infected plant is identified is to remove it quickly and dispose of the plant far away from the rest of the crop.
Bacterial wilts can also damage a plant badly. In some cases, bacterial diseases can be overcome by the plant. But again, for the home grower the best solution is to remove the affected plant and destroy it.
Fungal and mold are one of the largest groups of potential crop-damaging diseases. Blue Mold, various blights and fusarium wilt are the most common of this type. There are soil treatments that commercial farmers use to reduce the soil-borne fungal diseases, but the home grower can generally only use good crop management. Good drainage in the field will reduce the incidence of many of the soil fungi. Rotating crops to different fields and removing the debris from last year's crops from the field will also help. Watering directly into the soil or only wetting the leaves in the morning when they will have all day to dry out will help reduce fungal diseases.
Insect Pests
As you might imagine, a field of luscious, leafy and succulent tobacco plants is a nice target for a bug to live in, eat and reproduce. The commonly seen bugs that harm the plants are various caterpillers, aphids, leaf hoppers and nematodes in the soil.
The most common caterpiller pest is the tobacco or tomato hornworm Manduca sexta. These caterpillers grow to a very large size, 2-3 inches long and as big around as your thumb and result from eggs laid by the hummingbird moth (also known as the hawkmoth or sphinx moth). The moth usually lays the eggs on the underside of the leaves (then can vary in color from white to green) and when they hatch, the caterpillers take off eating! A hornworm can strip a leaf in a single day! Voracious! You can pick off the hornworms by hand when you see them or the damage they cause. You can also examine the undersides of the leaves for the eggs and remove them. There are several reports that hornworms can be seen flourescing at night under a black light (long wave UV), but I have not seen those confirmed as yet.
Other common caterpillers on tobacco crops are the army worm, cutworm and sometimes the cabbage looper, among others. Since caterpiller damage directly reduces the yield of your crop, strong measures are used to control them (see insect controls below).
Aphids are very tiny insects generally found on the underside of the leaf and may vary from white, through shades of green and even tan or brown. Aphids are sucking insects. There are mobile varieties which fly and ones which only move around on the plants. Damage from aphids ranges from making spots on the leaves to nearly killing the whole plant in extreme infestations.
Leaf hoppers move from plant to plant laying eggs which hatch into larva and suck sap until they transform to adult form. These bugs are a vector which can spread diseases, viruses and fungus across a field fast.
Nematodes are an insect that lives in the soil and infests roots. "Galls" on roots are an indication that you have nematodes. The best way to control nematodes is to rotate the crop into different fields annually and to plant other crops in those fields which aren't susceptable. Commercial farmers will frequently fumigate a field with an insecticide to control them. There are tobacco varieties which have been bred to be resistant to nematode infestation.
Insect Controls
The most common control of caterpillers (and sucking insects like aphids and leaf hoppers) is the systemic insecticide called acephate, trade name Orthene. While some control of leaf-eating insects is gained by use of topical insecticides such as Sevin, the sucking insects aren't controlled nearly as well or at all.
Beneficial Insects and Other Organic Remedies
Lady bugs are the most common beneficial insects used to reduce the aphid populations. They can be bought at various stores and released in the field. The larva are very good at eating aphids. If you broadcast an insecticide on your crop, you will likely be removing the ladybugs which could reduce the aphid population, thus requiring the use of a systemic to control the aphids.
bT (Bacillus thuringiensis) is an organically qualified bacteria which, when ingested by a young caterpiller, will disrupt it's feeding and kill it. bT requires reapplication after rains and since it is only useful on young caterpillers, must be applied before you see the larger ones. bT can be expensive to use.
Insecticide Soaps (for example Safer Soap) are primarily used to control aphids and require frequent application.
Diatomacious Earth or DE is claimed to be a natural insect control and should be investigated as part of a complete organic pesticide control.
That's a general overview of the pests, diseases and other maladies that can affect your tobacco crop.
Bob