When the angular velocity vector isn't in the same direction as the angular momentum (measured about the center of mass), the angular velocity will change direction over time. Is there a closed form for angular velocity and/or orientation over time?
I think you might be interested in the Poinsot constructions, see the corresponding Wikipedia article for an overview. For a slightly different angle at an answer to this question, have a look at this Mathematica Demonstration. In a similar vein, there's a fairly nice simulation here.
Long story short, there's no convenient closed-form solutions for the general case, but numerical solutions can be generated readily.
Addendum: The motion can, in principle, be described using Jacobian elliptic functions. This was published by Jacobi in 1850, in his paper "Sur la rotation d’un corps", in the German Journal für die reine und angewandte Mathematik 39:293–350. The PDF of the original paper is available here.
More references: A related question was asked on this forum, here. This document has some more suggestions for algorithms to describe rigid-body rotations. Googling "rigid body dynamics Jacobian elliptic functions" will reveal a wealth of additional information.