Brief Summary: The purpose of this study is to determine the safety and effectiveness of a multi-drug regimen (which includes prednisone, vincristine, cytarabine, doxorubicin, 6 mercaptopurine, and methotrexate) which is considered standard treatment for children and young adults with acute lymphoblastic leukemia (ALL), in combination with PEG-asparaginase and clofarabine to treat older adults with ALL. PEG-asparaginase has been used in chemotherapy treatment regimens for both children and adults with ALL. Clofarabine has been used in chemotherapy treatment regimens for children with ALL and has been shown to decrease the number of leukemia cells. Participants with leukemia that has an abnormal chromosome, called the Philadelphia chromosome, will also be given imatinib.

Detailed Description: * This research study has stages of treatment as follows: 1) Induction 2) Consolidation 1 3) Stem cell of Bone Marrow Transplant (if the participant is eligible). If the participant does not have a transplant: 4) CNS Therapy 5) Consolidation 2 6) Continuation Therapy. * During all phases of study treatment, participants will have additional tests and procedures to monitor their health and for research purposes. These tests will include: physical exams, blood tests, bone marrow aspirate/biopsy and EKGs (electrocardiogram) and/or ECHOs (echo-cardiogram). * INDUCTION STAGE: This stage lasts for about one month. The study drugs and the way they are administered are as follows: Prednisone orally on days 1-21 for participants less than 60 and days 1-7 for participants 60 or greater; Vincristine intravenously on days 1, 8, 15 and 22; Doxorubicin intravenously on days 1 and 2; PEG-Asparaginase intravenously on days 7 and 21; Cytarabine intrathecally on day 1; Methotrexate intrathecally on day 29; Imatinib orally on days 14-29 if participant has the Philadelphia Chromosome. * After induction, if there is evidence of ALL in the spinal fluid, participants may need to receive more intrathecal therapy. * CONSOLIDATION 1 Therapy: This stage will last about one month. Participants will receive Consolidation 1 Therapy, regardless of whether or not their ALL is in full remission after Induction. The study drugs and the way they are administered are as follows: Prednisone orally days 1-5; Clofarabine intravenously days 1-5; PEG-Asparaginase intravenously days 1 and 15; Imatinib continues orally for participants with the Philadelphia Chromosome. * After the participants blood counts return to normal, their bone marrow will be tested. If the bone marrow shows remission, participants will proceed to the next stage of the study. If the bone marrow does not show remission, the participants will no longer continue on this study. * STEM CELL or BONE MARROW TRANSPLANTATION: The next stage is stem cell or bone marrow transplantation if the participant is eligible. If the participant receives a stem cell transplant, they will receive additional chemotherapy (separate from the study drugs) followed by an infusion of stem cells. If the participant receives a bone marrow transplant, they will have a bone marrow aspirate and biopsy 3 months after the transplant and 12 months from the start fo the induction to monitor the status of the ALL. If the participant receives a bone marrow or stem cell transplant, they will continue to be a part of the study, but will not proceed with CNS Therapy, Consolidation 2 Therapy, and Continuation Therapy. * CENTRAL NERVOUS SYSTEM (CNS) THERAPY: CNS therapy will begin between 2 and 6 weeks following the end of Consolidation 1. This stage will last about one month. The study drugs and the way they are administered are as follows: vincristine intravenously on day 1; doxorubicin intravenously on day 1; 6 mercaptopurine orally on days 1-14; prednisone orally on days 1-5; PEG-asparaginase intravenously on days 1 and 15; methotrexate/cytarabine/prednisone intrathecally weekly for 3 weeks; imatinib orally continues daily if the participant has the Philadelphia Chromosome. * Radiation therapy will also be given during this stage of the participant is under 60 years old. The purpose of radiation therapy is to prevent ALL from coming back in the brain. Radiation will be given in 8 treatments, given once a day, and will be scheduled with other study treatment. * CONSOLIDATION 2 THERAPY: This stage begins as soon as CNS Therapy ends and lasts about 8 months. Participants will receive repeated cycles of the study drug treatment about every 4 weeks. The study drugs and the way they are administered are as follows: vincristine intravenously on day 1; doxorubicin intravenously on day 1; 6 mercaptopurine orally on days 1-14; prednisone orally days 1-5; PEG-asparaginase orally on days 1 and 15 (first cycle only); imatinib orally continues daily if the participant has Philadelphia chromosome. * CONTINUATION THERAPY: This stage begins at the end of Consolidation 2 Therapy. The goal of this stage is to get rid of all of the ALL in the body. Participants will receive repeated cycles of the study drug treatment every 4 weeks. It will last until the participant has been in remission for 2 years. The study drugs and the way they are administered are as follows: vincristine intravenously on day 1; mercaptopurine orally on days 1-14; prednisone orally on days 1-5; methotrexate intravenously on day 15; imatinib orally continues daily if the participant has Philadelphia chromosome.