I have heard talk of a few planes that are allegedly impossible to spin; maybe some of these 'self recover' from the stall before hand, or just don't even drop a wing, ever?
The only plane I have flown which is impossible to spin, and placarded so, is the Ercoupe. It has no rudder pedals, with the rudder being coordinated to the ailerons. And, the elevator is limited, so in most cases, you cannot pull it into a stall. If you do get it to stall or spin, and I have done both in it, you cannot hold it in, it just recovers on it's own. Other aircraft I have flown have control travels such that in some configurations, a pitch down in a stall is hard to achieve. But, as the aircraft can still be stalled in some configuration,s and still can be spun, they would not be classified as spin proof. Other types of modifications (like STOL kits) advertise that they improve stall spin resistance, and for my experience they do, but the aircraft can still be stalled and spun, and when you finally get it there, it can be a bit more sudden (it just held on to the bitter end longer).
A spin, in a suitable aircraft, is a benign maneuver, and well worth learning. A spin in a non spin approved aircraft may demand skill, and/or exceed limits during recovery. The Cessna Caravan upon which I did spin testing with an external load, recovered exactly as the design requirement states that it must. though in doing it, I came very close to both speed, and G limits during the recovery from the dive. The Cessna 206 is similarly unpleasant to spin.
Forward C of G spin in the Grand Caravan: