Yup, ideally no play.

In reality it's hard to get rid of ALL play, particularly in the smaller planes.

An overly large hole in a servo horn, a bit of lateral movement in the control rods, etc... all will cause a bit of play.

In something like a trainer, this is not a huge problem.

In a large surfaced plane, such as a 3D airplane, it can cause it to self destruct if flown too fast.

So in part it also depends upon which plane you are talking about.

Note:

If your linkages are otherwise tight, typically lateral bending or movement in the control rods is the biggest problem.

You can help to minimize this by installing a bit of wood against the fuse formers, etc. to "hold" the rods, preventing them from bending.

The rods can move back and forth freely, but the small wood piece with a hole in it for the rods, can prevent lateral movement.

Also check your servos. Sport servos, particularly the cheaper ones may have some play as the cogs can move a bit. This can lead to very slight movement, that translates to a larger movement on the control surfaces...