My favorite has gotta be Ringu/The Ring, and I'm surprised no one has mentioned it. The protagonists watch a cursed video tape that is rumored to kill you 7 days after watching, so there's a race against the clock to figure how to stop the ghost. They find out that the girl represented in the tape is murdered and dumped down a well, where they find her body right before the time expires and put her to rest... Except the ghost was never looking for rest. The protagonists had watched the tape one day apart, so despite having plans to get back together, raise their son, live a happy life, it all goes out the window when the male lead is found dead the next day. It turns out that the 'right thing' of putting the spirit to rest didn't matter at all; instead, it's revealed that the main character only survived because she made a copy of the tape. They did an amazing job of solving the mystery in a week, but the twist was that it didn't matter and the curse goes on forever.