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Many games have a console or menu option that toggles on a display of the current FPS. Games with 'timedemo' or benchmarking functionality can tell you the average FPS while running through a particular saved benchmark file.
For games that don't support either of these option, a program called FRAPS can be used to monitor the FPS (it can also be used to record video of a 2D/3D application). However, it eats up some CPU time, and so can impact performance of some games.