There are a number of oils that should not be used, or used very carefully in applications.
Phototoxic essential oils accelerate sun-damage on exposed skin. Care should be taken to use them carefully. A few that are phototoxic include Bergamot (except for Bergapten-Free types), Cumin, Ginger, Lemon, Lime, Lovage, Mandarine, Orange and Verbena.
Many essential oils can cause dermatitis or other skin irritations on some individuals. These include Allspice, Aniseed, Basil, Black Pepper, Cajeput, Caraway, Cedarwood (ALL types), Cinnamon, Clove, Eucalyptus, Garlic, Ginger, Lemon, Parsley, Peppermint, Pine Needle, Thyme, and Turmeric. These oils should be diluted to three times the normal dilution. If you are sensitive to these, you should not use products that contain them. Again, always do a patch test.
Certain essential oils can cause sensitization. Sensitization is when the skin becomes easily irritated. If your skin has a tendency to become irritated easily, you should avoid such as basil, bay laurel, benzion, cedarwood, chamomile (both kinds), or citronella. Garlic, geranium, ginger, jasmine, lemon, lemongrass, peppermint, orange, tea tree, thyme, vanilla, and Ylang-Ylang are among others that can sensitize skin.