Polarizers can be useful for removing shiny reflections in water and the like. However, their purpose for increasing color saturation and darkening skies seems less relevant in the digital age. I met a guy on my travels once who had a circular polarizer permanently fixed to his zoom lens. They are sometimes hard to remove without a special tool or improvised lasso made from rough string. I helped him free up some space on his flash cards by burning his images on my laptop and noticed that many of his images were simply not sharp. I can't remember now whether a polaraizer robs you of one stop or two stops exposure, but in a situation of grey skies and dark ruins where you probably want as much DoF as possible and are probably using f11 or f16, perhaps even f22, you don't want to reduce the amount of light entering the camera unnecessarily.
If you are able to use a tripod, then auto bracketing of exposure and digital blending is a better solution. If you always shoot in RAW mode, as I do, you'll find with a grey sky like the one in your shot at Angkor, you can probably recover a lot of detail by doing an 'underexposed' conversion and blending it with an 'overexposed' conversion Alternatively, you can 'select' the sky with the magic wand and just darken it in levels. Finally, if you see detail in a grey sky at the time you take the shot (and it's something you really should notice), then make sure you slightly underexpose the shot.
When all else fails, I'm afraid you'll just have to replace the uninteresting sky with a more interesting one in Photoshop .