If you are found to be eligible to take part in this study, you will receive carmustine through a needle in your vein over 1 hour on Day 1. On Days 2-5 you will be given cytarabine by vein over 1 hour and etoposide by vein over 3 hours. This will be repeated every 12 hours on Days 2-5. On Day 6 you will be given melphalan by vein over 30 minutes. On Day 7 the stem cells that were collected earlier from a donor will be given back to you ("transplanted") through your catheter over 30-45 minutes. You will also receive rituximab by vein, over 5 to 7 hours before the transplant and then weekly, for a total of 4 doses. In addition, if you are receiving a matched unrelated or mismatched donor transplant, on days 5-6 you will also be given thymoglobulin by vein over 4-6 hours. Patients with T-cell lymphoma will not receive Rituxan.