What could cause a planet to have apparently random season lengths? The world A Song of Fire and Ice series is set on is characterized by seasons that last several years (how years are measured on this planet is not specified to my knowledge).  However, they are of unpredictable, variable lengths, though seemingly in balance (long summers are followed by long winters).  Rather than some sort of massive El Niño, it seems to be a result of something astrophysical, as winter can be forecast by the shortening of days.
Is there some possible mechanic for this or is it outside the realm of possibility?
 A: N-body problem should pretty well cover this. Solving the almost intractable problem of three gravitating mass goes back to Newton.
http://en.wikipedia.org/wiki/N-body_problem#Three-body_problem
Quoting from the above article: "Specific solutions to the three-body problem result in chaotic motion with no obvious sign of a repetitious path."
So assuming three orbiting bodies in chaotic motion, one could predict aperiodic seasons. Hence, yes, there should exist somewhere in this universe a planetary system with random season lengths.
A: The seasons on earth are caused by the rotation of the earth around the sun in addition with the inclination of the axis of the earth. This causes the angle of incident sunlight to be lower in winter and higher in summer. 
Now, the inclination of the axis of the earth is pretty constant. But if that axis would shift in some funny way, you could have any season any time. So, for a summer that lasts several years, the axis would have to shift so that the light incident on a given hemisphere remains at a high angle.
However, even defining a year might be hard on such a planet. On earth, we think of a year as the time it takes for the earth to circle the sun once. But that is not how ancient civilizations measured it. They looked at the height of the sun in zenith and noted that there was a day when the sun stood highest, and a day where the sun stood lowest, and these are summer and winter solstice, respectively. With the earth's axis's angle fixed, the time span from one summer solstice to the next is the same as the time it takes for the earth to completely circle the sun, but in our imaginary planetary system, these two movements would not be related anymore. But with random axis movement, it might be impossible to tell when a circle around the sun is completed...
A: IANAA, but a way to do this could be to have the planet have a very long orbit (centruries) but have the axis of rotation precess chaoticly on the time scale of a decade. To have chaotic precession on the decade long scale we need, there would have to be a very large object nearby. For example, Hyperion (a moon of Saturn) has an axis of rotation that precesses chaoticly on the scale of 40 days. The planet of A Song of Ice and Fire has a moon, but this would only be a weak perturbation, which would lead to chaos on a time scale much longer than a decade if its chaotic at all. The earth's axis does flop around but on a very long time scale (and some random Google hits say its not chaotic, for what thats worth)
The other issue is that if the axis is precessing randomly then you would expect to have it end up everywhere, say with north pole stuck pointing at the sun. This would lead to half the planet being in a decades long day and the other half in a decades long night. Which is not in the book. So you need to find some mechanism that keeps the axis of rotation approximately perpendicular to the plane of orbit. Maybe two similarly sized planets with approximately aligned axes of rotation perpendicular to the plane of orbit? Conservation of angular momentum would make large deviations hard I would guess.
So its not too physical plausible... but its more physically plausible than a wight?
A: I don't think orbital dynamics allows for it. You could postulate that it's star might be an irregular variable star, whose intensity chaotically changes. Then the seasons would be more or less global. I don't know if any chaotic variable stars would have had an evolutionary history such that an inhabitted planet is a possibilty (i.e. a stable enough climate long enough for life to evolve), most likely not. But, it is a work of fiction not fact.
