I love "inspired by true events" movies - so it will come as no surprise that APOLLO 13 is my all-time fave.
If you want a few more to chew on before you rent - here are a few more that are awesome (not based on true events):
THE USUAL SUSPECTS: A boat has been destroyed, criminals are dead, and the key to this mystery lies with the only survivor and his twisted, convoluted story beginning with five career crooks in a seemingly random police lineup.
SAFE HOUSE: A psychological thriller; Mace Sowell, an ex-intelligence operative and whose past government activities catches up with him.
FRAILTY: Fenton Meeks (Matthew McConaughey), comes forth to tell the FBI that his brother Adam may be the serial killer who calls himself God's Hands, who the FBI has been searching for. The film uses flashbacks to show Meeks' childhood with a father (Bill Paxton) who believed he was on a mission from God to destroy demons that inhabit human bodies. Fenton saw his dad as evil, while Adam saw him as a hero.
HIGH CRIMES: High-powered lawyer Claire Kubik finds her world turned upside down when her husband, who she thought was Tom Kubik, is arrested and is revealed to be Ron Chapman. Chapman is on trial for a murder of Latin American villagers while he was in the Marines. Stars Ashley Judd, Morgan Freeman and James Caviezel.
THE SECRET WINDOW: Johnny Depp is fabulous as a writer accused of plagiarism by a strange man, who then starts haunting him for "justice."
ABOVE SUSPICION: A Cop is paralyzed in a shooting and unable to walk. His misfortune brings him sympathy, which he uses to devise a plan to rid himself of his unfaithful wife and her lover.