well since your shutters are burgundy I would paint my door a hint darker then the color on the shutters and make a grand entrance;)
Power blue is a great mix - My house inside and out is power blue and I use burgundy and cobalt as accent colors - the gray takes on the blue as a wonderful mix
A nice, rich cream would make your door stand out. It would be a twist on the traditional "Americana" color scheme. Here's an idea for how it could all come together. http://deeconstructed.com/quick-curb-appeal/ Good luck!
I think that a matte/satin finish black door is always attractive.
Have you tried a dark wood ? Think about wood with a dark burgundy tone. Then use a high gloss like boat lacquer to add protection from the elements.
A lot depends on if your door is recessed or gets plenty of light. You don't want a dark color if it is in an alcove like some of these houses have. Buy up some sample jars and test the colors. If you can use it, a flat charcoal would be lovely! If you are limited on light, try gray with the woodwork painted white! My front door is recessed and it is painted the same color as the house with white accents.
BLACK WOULD BE NICE.
@Sherry F you didn't mention if you had a garage door and the colour of it if you have one. Personally, I am agreeing with those recommending black - or a slate grey - it would go well with your grey house and burgundy shutters.