 This research study examines the safety and feasibility of aspirin with or without Simvastatin in solid tumor patients at risk for VTE Venous Thromboembolism - or blood clots - in the arms, lets, lungs, or other part of the body. One-fifth of all thrombotic clotting events occur in patients that have cancer. Changes in sP-selectin will be used as a measure of efficacy. We have chosen sP-selectin as the primary marker because of its role in hemostasis, because it is predictive of thrombosis in cancer patients and because of promising preliminary data. We expect that sP-selectin levels will be elevated in patients before therapy with aspirin andor statin, but that these levels will fall significantly during treatment, rise during the observation phase, and fall during the second study period. Patients who take part in the study have been diagnosed with a solid tumor cancer and are considered to be intermediate to high risk for VTE. The standard of care is to give chemotherapy for solid tumors and treat clots which develop using blood thinners. 