The following is composed of only some of the more popular legal alternatives available (this is not a complete list!). Mississippi State University endorses the use of these solutions only in that they provide legal methods for downloading music/movies; MSU does not endorse any specific commercial product.
The RIAA provides a list of many legal music alternatives on their dedicated Why Music Matters page.
Movies & TV
The MPAA provides a list of many legal movie and television alternatives.