Is there any situation in which DNA is made based on a RNA template? What is the enzyme included?

The process in which DNA is synthesized having as template a RNA chain is known as reverse transcription. In cells infected by retroviruses (RNA viruses, like the AIDS or SARS viruses) reverse transcription happens and DNA is made from information contained in the viral RNA.

Viral RNA within the host cell forms DNA with the help of an enzyme called reverse transcriptase. Based on that DNA the host cell then makes viral proteins, new viruses are assembled and viral replication happens.

Nucleic Acid Review - Image Diversity: reverse transcription