Final answer:
Programs from LBJ's presidency that still exist today include Head Start and Medicare. The Civil Rights Act remains a cornerstone of anti-discrimination law, while the Apollo Program has concluded but has a lasting legacy.
Step-by-step explanation:
Of the programs introduced during President Lyndon B. Johnson's presidency, several still exist today. Specifically, the following programs continue to operate: a) Head Start, which is a preschool program providing educational services to young children from low-income families; c) Medicare, a health insurance program for the elderly and certain individuals with disabilities; and, while the Civil Rights Act is not a program but rather a significant piece of legislation, it provided the legal framework to end segregation and prohibit discrimination, having a lasting impact that still influences society. The Apollo Program was a historical project that landed humans on the moon but has since concluded. However, the legacy of the Apollo Program lives on in current NASA missions and space exploration endeavors.