No. 5 Biohazard 4
Biohazard 4 isn't too bad at pausing, but it has some strange idiosyncrasies. You can't pause the game during the following situations...
-firing a gun
-kicking
-180º turn
-lying on the floor after being knocked down
-being hit by an arrow or Melee weapon
-jumping over a gap
None of which are a too much of a problem game play wise, which is why I've put it at no.5.