The purpose of this study is to understand how changes in the immune system of HIV-infected patients affect their risk for 3 serious infections: Pneumocystis carinii pneumonia (PCP), cytomegalovirus (CMV) retinitis, or CMV organ disease. The purpose also is to understand how anti-HIV medicines may improve the immune system in these patients. (This purpose reflects a change in the AIDS-related [opportunistic] infections studied.) Presently, HIV-infected patients who have had PCP or CMV disease stay on lifelong therapy to prevent the return of the disease. This study is trying to see if a special lab test can help identify which patients can stop this preventive therapy without having another episode of PCP or CMV organ disease. (This rationale reflects a change in the AIDS-related infections studied.)