A demo version of Epic Games’ Unreal Tournament 3 is included with the Unreal Development Kit download. The demo ships with four levels, three weapons, four vehicles and one robot character for your sampling enjoyment.
The UT3 editor is widely used for learning Unreal Engine technology, and now there is UDK, which gives you all of UT3’s game creation tools in addition to high-level engine features developed since the game’s release.
UT Demo is a great example and starting point for those looking to develop their own first-person shooter experience.