That's the dew freezing on. If you throw a waterproof cover over the windshield, hardly any dew will accumulate, and the problem will be mostly nil. The closer the cover hugs it the better.
Using a waterproof cover is your only foolproof solution.
I have had (partial) luck with spraying wiper fluid last thing before leaving the car. Less dew sticks, and the few pieces just wipe away in the morning.
Cover your windshield with aluminium:
Applied on a windshield, your car will look like this:
It will prevent any dew freezing on in most scenarios (it won't work against heavy snowfall and blizzards, naturally).
However, even if a lot of snows falls on top of it, removing the cover will still take care of most of the freezing.
If you leave your car uncovered outside in freezing rain, it will ice up just like everything else. Sorry, but the only solution there is to cover it.
For snow however, you can greatly reduce and in some cases eliminate ice build-up by just making sure your windshield is cold before allowing any snow to fall on it. Ideally, this means parking your car and letting it cool for a few hours before the snow starts falling, but if it's cold enough outside you can speed this up by turning off the heat and opening your windows for the last part of the drive home. You'll still end up with some heating from the engine, unfortunately. Also, make sure you have a good hat with you.
While I am not sure how well this will work with icing problems, try a product called glass wax. It is good for keeping moisture and bugs from sticking to the window, and may just be effective enough to make your problem bearable.
A mixture of water and vinegar is supposed to remove ice and prevent ice from forming. see How to remove ice from windshield for more.
The best solution is to get the car into a garage or carport if possible. Surprised no one has mentioned that so far. Some sort of roof over the car is really helpful.
If not those are available, then natural shelter like large trees could be helpful, in addition to covering the windshield like described in other answers. I've also seen cars parked next to ventilation or air condition vents to re-use the warmer air, but you got to have some luck for that to be available.
Just cover your front windshield with a rubber bottomed bathroom mat/rug...its not perfect but it should help out in the mornings.
Keep a blowdryer and extension cord around. Blowdryers work well for getting doors unstuck and locks unfrozen too.
I've never done this, but I'd like to suggest an idea I just had:
Cut four 1" slits in the corners of an electric heating pad, then slip in four neodymium magnets that have velcro dot stickers (into each individual slit) and adhere to the inside of the pad lining. Then individually stick the---now---magnetic corners to the window within the vehicle to four other matching neodymium magnets on the outside of the window, and connect this to an extension cord.