Selumetinib in Cancers With BRAF Mutations

Inclusion Criteria: * Ability to understand and willingness to sign a written informed consent document * Histologically confirmed metastatic or unresectable solid tumor * Results from tumor tissue analysis that show a glutamic acid-for-valine substitution at amino acid position 600 in the BRAF gene (V600E) or other activating BRAF mutation, as determined by high-throughput genotyping * Patients may have received any number of prior systemic treatments for their cancer * At least one measurable site of disease by CT, according to standard RECIST criteria 1.0 * ECOG performance status 0-1 * Absolute neutrophil count \> 1500 per cubic mm * Platelet count \> 100,000 per cubic mm * Hemoglobin \> 9 g/dl * Serum bilirubin \< 1.5 x upper limit of normal * Serum AST and ALT \< 2.5 x upper limit of normal (=\< 5 x upper limit of normal, for liver metastases) * Serum creatinine \< 1.5 x upper limit of normal * For women of childbearing potential, negative serum pregnancy test and use of physician-approved method of birth control throughout the study Exclusion Criteria: * Estimated life expectancy \> 12 weeks * Patients with melanoma * Have received chemotherapy or radiotherapy within 4 weeks prior to entering the study (6 weeks for nitrosoureas or mitomycin C), or a targeted therapy within 2 weeks prior to entering the study * Have not recovered from adverse events due to agents previously administered (CTCAE v3 grade 1 or baseline) * Currently receiving other investigational agents * Known brain metastases, unless treated and stable off of corticosteroids for at least four weeks * History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD6244 * Prior treatment with a selective inhibitor of RAF or MEK (e.g., RAF265); (note: prior sorafenib is allowed) * Uncontrolled intercurrent illness, including but not limited to: * Clinically significant active infection * Symptomatic congestive heart failure, unstable angina pectoris, and/or cardiac arrhythmia other than atrial fibrillation * Psychiatric illness/social situations that would limit compliance with study requirements * Refractory nausea or vomiting, swallowing disorder, or malabsorption syndrome that would interfere with swallowing or absorbing the study medication * Pregnant and/or breast-feeding women * Previous or concurrent malignancy, except for the following circumstances: * Disease-free for at least three years and deemed by investigator to be at low risk for recurrence of that malignancy * Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin) * History of solid organ transplantation or other condition requiring the use of immunosuppressive medications * Uncontrolled hypertension (systolic BP \>= 150 or diastolic BP \>= 100 that cannot be controlled with medications) * A mean left ventricular ejection fraction (LVEF) less than 45%