Intense femtosecond VUV, XUV, and X-ray pulses from free-electron lasers (FELs) enable time-resolved experiments studying ultrafast dynamics in a large variety of systems relevant, e.g., to physics, chemistry, biology, and material sciences. In this paper, we focus on time-resolved studies of gas-phase molecules, which lie at the crossroad between atomic, molecular and optical physics and ultrafast photochemistry. We describe the current status of the field and discuss typical experimental configurations used for pump-probe experiments with FELs. We illustrate them with three recent examples for such experiments performed at the FLASH and LCLS FELs studying charge transfer following XUV and X-ray photoabsorption as well as photoelectron diffraction from aligned molecules. We conclude with a short outlook on future developments and perspectives for femtosecond pump-probe experiments with FELs.