This wingless insect is typically active during the warm weather months and it will feed on many different types of plants besides the basil. Since basil is too sensitive for the vast majority of pesticides, the only real recourse you have against this pest is to wash it off when you see it.
Nematodes are roundworms so small that you need a microscope to see them. You have to watch the basil plant for certain symptoms, such as wilting, to identify the problem. Nematode damage can be countered by adding more nutrients to the soil around the plant.
Slugs often come out during rainy and damp weather and will chew holes right through your basil plants if you don't take care of them. An article on Gardens Alive claimed there were at least 13 homemade remedies, including beer and coffee. If you don't see the slugs, examine the plant closely for slimy trails on the leaves.
On the whole, deer generally ignore herbs in favor of other garden plants. However, if a deer is attracted to basil it will eat the whole plant. Only a complete fence is guaranteed to keep the deer away.
Whiteflies feed from the sap of the basil plant. They're doubly dangerous because they leave white residue behind on the leaves that can interfere with the plant's ability to absorb sunlight. If you don't see the whiteflies themselves, other symptoms of a whitefly infestation includes dropping and yellow leaves.