If we knew what engine(or API if any) you are using to make a game, we could give more specific suggestions. Example, if you are using UDK or the freshly released UE4, you would be best with using the Matinee editor that is integrated into the software, which renders real time the cinematics you set up.

If you are using Unity, you could either script it out(for real time usage), or pre-render a video and render that in your game. Many other engines/APIs have some sort of video rendering capabilities as well so you could go that route with them as well. In many cases though, you would script it out in your game itself, using game graphics real time.

Assuming you want to go with pre-rendered video, Blender is the best "free" way to go about it, especially if you happen to be using it for creation of 3d models for your game. You could use higher end software as well if you have access to it. 3dsmax and maya can also do video rendering. Blender has a video editor integrated as well, though other software does not and so you would have to get a video editor in order to put together your scenes/video.