How can I attack to different portions of the screen? Often times in video games that use melee combat, there are three or four preset animations that play through when you swing your weapon; however, the higher end games have different strokes that play depending on which way you are moving your mouse or have recently moved your mouse, effectively giving you the ability to control where you attack, and requiring more skill.

How would I implement this in the Blender Game Engine? I want to play a different animation or attack based on which direction my mouse has just moved.
After trying to solve this problem by myself for almost my entire blender career, I stumbled across a solution. This is a no python approach.

The basic idea is to have an empty, offset from the player, and "slow parented" to the player that two specialized bones track toward. By animating a normal downward chopping motion, as well as the influence value of the track-to bone constraint, we can cause the player to chop across in his upper arc.
This comes at the expense of variation as the player can't chop up from a downward position or thrust.

Step 1

For you basic setup, you will need to create three extra bones: one for each shoulder, and one that control those two so they don't point inward. You will also need to create a "plain axis" empty that the control bone tracks to. 
Add a track to bone constraint on the control bone and set it's target as the empty, which will need a slight upward and forward offset (see figure 1). Parent it to the player and give it some slow parent value.



figure 1



Step 2

Animate your chopping motion; it should provide all the functionality you'll need. note: do not animate the shoulder bones as this might interfere with the essential tracking.
Also animate the influence of the track-to constraint, starting at 1, staying at 1 until shortly before the end, and then moving to 0.



Step 3

Switch to the logic editor and add a mouse-click sensor, an AND controller, and a Action actuator, set to play mode and with the chopping/turning of the shoulders action.



Viola! looks a bit awkward, but hey, that's the cost of beheading people.



(edit) you will also need a run-armature actuator