They made this simple in 2010. In 2007 it isn't.

If you get this wrong you may lose the recent list altogether, make sure you pin the ones you need and don't set the number to less than this.

In the recent list click the pins (make them green) for the programs you WANT TO KEEP.
Count the green pins.
In PowerPoint Options > Advanced > Set Number of Recent Documents to the number you counted and OK.

Only the green pinned docs should be left.

Set the recent number back to whatever you need.