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5 Answers
Achilleas Vortselas
Achilleas Vortselas, not a physicist (an engineer)
When defining "slipperiness", one has to ask, "Compared to what?"

Adhesion between surfaces is known to be related to surface energy [1] (or equivalently, surface tension [2] in liquids). If having two contacting surfaces bond results into less energy overall than them being in contact with the environment, then these will adhere.

Furthermore, adhesion between hydrophilic materials is enhanced in humid environments, because of the meniscus effect, in which the surface tension of water droplets at the interface of the asperities of the two materials adds to the attractive (adhesive) force of contact [3].

High surface energy materials such as metals and ceramics, which are also hydrophilic, are "sticky" because their surfaces attract each other in contact and the strong water meniscus augments the attractive force. Low surface energy materials, such as polymers [4] are "slippery" because they don't attract each other so strongly and they repel water.

Now ice has the following surface energies:
Ice-water: 33 dyn/cm
Ice-vapour: 109 dyn/cm
Water-vapour: 76 dyn/cm (the difference of the previous two)

This makes ice more "friendly" to water than it is on itself. Water will penetrate an ice-ice interface as far as the water-ice contact angle will allow: [6]
[math]2cos{\theta}_0=\frac{{\gamma}_{ss}}{{\gamma}_{sl}}[/math]

Because of the above surface energy values, this angle is close to zero. In practice this is observed on melting ice, where water forms veins, among the ice crystals. [7]

Ingress of water meniscus in ice interface [7]

The meniscus effect is working on ice too, however ice is either too cold and causes humidity around it to freeze, or melting in which case it becomes a source which, given some friction, readily saturates the contact with water.

When the latter happens, the meniscus effect collapses. Quoting from [8]:
It has been experimentally observed that a wet snowpack will remain stable at low saturation levels (up to 7%); all free water is attracted to the interfaces between the ice particles by capillary effects, and surface tensional forces through the liquid draw the particles together. This is classified as the pendular regime – the water forms pendular rings at the points of contact between the particles, and the air is connected throughout the pack. When the saturation level rises above 7%, however, the air is no longer connected; it exists in pockets throughout the snowpack and the water is connected through the medium: then snow behaviour becomes more fluid-like, tensional forces disappear, and the snowpack becomes  unstable. This is known as the funicular regime.

What I am gathering from all this is that ice is "slippery" because it is never completely dry (see the article linked by Michael Betancourt) and this has the effect of reducing its friction, instead of increasing it, as with the materials we usually see around us.

Ice is also exhibiting superlubricity (very low coefficients of friction) when sled against metallic materials like steel (μ=0.005).  This very meticulous study [9] is attesting the effect to the combination of high hardness and low shear strength that ice exhibits and not on frictional melting, based on the experimental observation that the coefficient of friction depends on the crystallographic direction (from experiments on skating rinks with single crystal surfaces!).

References:
[1] Wikipedia: Surface Energy.  http://en.wikipedia.org/wiki/Sur...
[2] Surface tension, definition, units and data for water at various temperatures: http://www.engineeringtoolbox.co...
[3] B. Bhushan, Modern tribology handbook, CRC Press, 2001.
[4] Surface energies of common materials, see Table on p.3: http://www.flexcon.com/Converter...
[5] Physical properties of ice: http://www.its.caltech.edu/~atom...
[6] J.S. Wettlaufer, Ice surfaces: macroscopic effects of microscopic structure, Philosophical Transactions of the Royal Society of London. Series A:Mathematical, Physical and Engineering Sciences. 357 (1999) 3403 -3425.
 http://earth.geology.yale.edu/~j...
[7] Nye J.F., The rotting of temperate ice, Journal of Crystal Growth. 113 (1991) 465-476.
[8] J. Barlow, Mathematical Modelling of Snow, http://www.enm.bris.ac.uk/teachi...
[9] Katsutoshi Tusima, Adhesion theory for low friction on ice, http://www.intechopen.com/source...
Michael Betancourt
Michael Betancourt, BS Caltech, PhD MIT
The "pressure-melting" theory has fallen into disfavor lately as the effect is too small to induce any noticeable melting in practice.  Slipperiness is instead thought to come about in two stages: first the surface of all ice is bound to the bulk only weakly because the crystal is incomplete, second the friction of any shear force is enough to break these weak bonds and produce the slipper layer of water.  Physics Today had a nice review a few years ago, http://lptms.u-psud.fr/membres/t....
Bryan Beal
Bryan Beal, Physics hobbyist.
Physicists used to believe the "slipperiness" was the result of the pressure of an object coming in contact with ice, causing a thin layer to melt and lubricate the pressurizing object. That theory is now coming into doubt.

A newer and generally accepted theory is that molecules of frozen water that come in contact with air can't bond to the molecules of the ice beneath but rather stay in a kind of 'semi-liquid' state. These molecules remain in a semiliquid state and provide lubrication regardless of pressure from an object.

Wikipedia has more good info. http://en.wikipedia.org/wiki/Ice
Tried asking Feynman?

I'm not totally sure, but i guess it's the same effect like on ice skates: The movement causes a thin water layer on wich you float onwards.

edit: other answers proved me wrong
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