Only the iOS (iPhone/iPad) platform currently has a built-in video record feature. However, if you run the app on Windows or Mac, there are several tools you can use to record the screen during playback, and then you can make a video of your sims. One quick-and-dirty way (that looks great!) is to use your cell phone or other camera and simply record the screen. Here is a great example of this.
aTube Catcher (Free) A solid, easy-to-use screen capture utility with format conversions (as well as a great tool for downloading video content from the Internet (Thanks Louis S. for trying it out and recommending it!)