This would be very useful so that the player can skip cutscenes/cinematics that they've already seen. Every time I respawn on my levels, I have to read through screen text and dialogue over and over again.
For not going through certain cutscenes again, you can use variables with the "s_" prefix; these variables are global and keep their values when you die (all others are reset to 0). However, the music will always be reset to the default track (chosen from the Course Properties window), so you should put "Set Music" triggers at respawn points if necessary.