Skin cancer may be divided into two types: non-melanoma and melanoma.
Nonmelanoma Skin Cancer
There are two major sub-types of non-melanoma skin cancer:
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Basal Cell Carcinoma- The most commonly diagnosed skin cancer. Tumors often develop on regions of the body that receive regular sun exposure such as the face and hands. Due to its slow growth rate, basal cell carcinoma rarely spreads and is usually treatable.(1) A common form of basal cell carcinoma is nodular basal cell. Lesions appear as a pearly nodules in various colors including brown, black and blue.(2)
Some examples:

Images used courtesy of the Skin Cancer Foundation.
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Squamous Cell Carcinoma- Appears on body parts that experience increased levels of sun exposure such as the face, lips and back.(1) This cancer is more likely to spread than basal cell carcinoma. The cancerous lesions have numerous forms. They may be rough, scaly, lumpy or flat. Blood vessels may appear at the edge of a lesion causing it to bleed easily.(1)
Some examples:

Images used courtesy of the Skin Cancer Foundation.
Melanoma
Melanoma is a cancerous growth of melanocytes and most frequently develops in the skin.(3) Melanoma may also develop in other parts of the body that contain melanocytes including the meninges, the digestive tract, the eyes and lymph nodes. The following descriptions are limited to melanoma of the skin.
There are several types of melanoma that can be categorized based on their appearance, either with the naked eye or microscopically:
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Superficial spreading: The most frequently observed melanoma. This form may develop in any region of the skin. Lesions are usually raised around the edges and a brown color with hints of pink, white, gray and blue.
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Nodular type lesions: Also arise on all regions of the body and are typically black or brown in color.
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Acral lentiginous lesions: Characterized by flat, brown or black tumors that often develop on the hands and feet.
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Lentigo maligna melanoma: Develop on an individual's face. Distinguished by its irregular border and tan to brown color.(4)
Some examples of melanomas that demonstrate the irregular shapes and colors often encountered:

Images used courtesy of the Skin Cancer Foundation.