AZD6244 With Cetuximab for Solid Tumors and Colorectal Cancer

Background: \- The experimental cancer treatment drug AZD6244 has been shown to block signals that tell cancer cells to grow. Cetuximab, a drug approved to treat cancer of the head, neck, colon, and rectum, also blocks signals that tell cancer cells to grow. Researchers are investigating the highest safe dose of AZD6244 to give with cetuximab, and will also investigate the effectiveness of this drug combination in individuals who have colorectal cancer that involves a particular protein known as the K-RAS protein. Cetuximab is not used to treat colorectal cancer with K-RAS tumors because it has not been shown to be effective, but researchers believe that adding AZD6244 to cetuximab may improve how well cetuximab works, even in people with K-RAS tumors. Objectives: * To evaluate the safety and effectiveness of AZD6244 in combination with cetuximab for solid tumors that have not responded to standard treatment. * To evaluate the safety and effectiveness of AZD6244 in combination with cetuximab for colorectal cancer that involves the K-RAS protein and has not responded to standard treatment. Eligibility: * Individuals at least 18 years of age who have been diagnosed with solid tumors that have not responded to standard treatment. * Individuals at least 18 years of age who have been diagnosed with colorectal cancer that has not responded to standard treatment. Design: * This protocol will involve two separate studies: an initial study to establish the highest safe and effective dose of AZD6244 and cetuximab in individuals with solid tumors, and an expansion study of AZD6244 and cetuximab in individuals with colorectal cancer involving the K-RAS protein. * Participants will be screened with a full medical history and physical examination, blood samples, imaging studies, and other tests as required by the researchers. * AZD6244 is a capsule to be swallowed once or twice a day, every day, with water on an empty stomach. Cetuximab will be given intravenously once a w