So far we've heard of two "spinners" - Cherokee 140, and C-172...both metal trainers. If this is truly the case, it's further irony how airplanes that have been designed to be aerodynamically forgiving to the lowest-common denominator are just the opposite under certain conditions. I will take my aerodynamically neutral "unforgiving" Pitts any day. It'll easily recover from anything you ask it to, and also do anything you ask, except spin out of a full slip it seems.
I found it difficult to get C-172s to do this, if at all, power off. I keep noticing in the thread that the people who are arguing that most trainers "won't do it" are talking completely power-off, in a descent for a landing... and those saying "it will do it!" don't specify.
Add some power, usually all of it, and it'll whip right over.
I'll specify for my experience. It required power. All of it at my altitude up here, and power on, a C-172 will go right over the top and enter the spin toward the up-wing side. Someone else here alluded to it... they said their instructor set up for a "departure stall"... power all the way up, get the yoke back in your lap, slip like mad, and it'll break "over the top". Relatively slowly.
Most C-172s I did it in, liked going left more than they liked going right. Right would take a rediculously long time to develop.
One airplane (that was probably out of rig... it didn't particularly fly straight even after much screwing around with the rudder trim tab -- I hate junk rentals...) would be particularly snappy entering to the left, and it was the aircraft we shot video of.
And the video... of course... is long gone, lost in a move many years ago...
Didn't really try it, but I suppose you might get a Skyhawk to do it, set up for lower or no power, if you really yanked from fast level flight trying to force an accelerated stall, but you're just abusing a Skyhawk doing that...
And if anyone's doing that much yanking in the pattern, they probably deserve to end up in a pile of sheet metal off the end of the runway, anyway.
I'd love to go see what a older straight tail 150 would do... those are spinnin' little fools, and the non-swept tail had more rudder authority than the later swept tails.
But around here, two guys in a 150 or 152 with half tanks is barely going to get off the ground on a summer day anyway, so I had to move over to a 172 very early in flight training.