newtonian mechanics - Can precession happen with no external forces?

I wanted to ask the following question:

Can a body that experiences no forces whatsoever precess? Let's say I have a body in space - no gravity or anything - can I make it precess without applying any forces or torques? If so, how? Under what conditions? What would its movement look like? Could you give an example of something like this?

Answer

Allow me rephrase your question, it seems to me that the following formulation is closer to the case you are thinking about:

In the absence of any external force, can a rigid, axially symmetric body move in a way so that its motion is not axially symmetric?

(Of course I phrased the question that way specifically for the answer to be 'yes'.)

A spinning axially symmetric object can have a sustained wobble. The nature of this wobble is that the symmetry axis sweeps out a cone. This wobble can just as well occur on top of a precessing motion, in which case the wobble is called 'nutation'. When a qyroscope wheel is in a combined precession and nutation motion the amplitude of the nutation motion is smaller than the amplitude of the precession motion, and the frequency of the nutation is higher (in most cases far higher) than the frequency of the precession motion.

For the wobble in the no-external-force case:
One might have the expectation that when you throw some object, giving it a spin, then at the instant that you let go the object settles to a non-wobbling spin. But in fact an object, when thrown with spin, can and will have a sustained wobble if that is how it happened to be thrown.

There is a story known as 'Feynmans wobbling plate'. Feynman was sitting in a cafeteria of the University where he had a teaching position, and as Feynman recounted:"some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling."

There's a youtube video, titled Feynmans wobbling plate. It shows some footage of an actually thrown plate, followed by a mathematical discussion of the rotational dynamics.

Remark:
In my rephrased version of the question I added the condition 'axially symmetric body' because that is a case where one might perhaps expect that it cannot wobble - whereas in fact it can. By contrast, the two earlier answers to this question discuss less symmetric shapes, where you do expect complicated tumbling motion.