As graphics hardware has improved, developers have had more and more polygons to work with in any particular scene. During this same time of visual enhancements, many lead designers seem to have developed a rather unhealthy desire to see corpses more violently mutilated in their daily gaming experiences. Dismemberment satisfied these two expanding ideas quite well.
Dismemberment, while not a new idea, is used more frequently now than it used to be, showing up in any game where the console can take the performance hit of simulating appendages flying around in 3D space. Certain series, however, have been using this effect throughout their existence, most notably the LEGO games, where characters always have and continue to lose arms, hands, and legs for comedic effect.
Note: "Dismemberment" refers to any game where limbs can be physically removed from their rightful owner. If dismemberment is tactically relevant enough for the player to use it as an advantage in combat, the game has Strategic Dismemberment.