There are a number of general aviation aircraft with trimmable
horizontal stabilizers that are capable of being mistrimmed to the point
that control is compromised (as are, of course, virtually all jets with
big, powerful trimming stabilizers and relatively small elevators).
The Cessna 180/185 series is a good example: unless you have a pretty
good load in the back seats or baggage compartments, it can _only_ be
landed three-point if the stab is trimmed just about all the way back on
final (necessitating forward pressure to hold final approach speed).
With anything less, there's just not enough elevator authority to
overcome the stab, and a half-assed wheel landing (with bounces) is
usually the result.
Similarly, early jets like the 707 could very easily run out of
elevator authority (one reason the elevator was kept small was to
provide manageable forces for the crew, since actuation is good ol'
cables and bellcranks). Note that this doesn't mean that the forces
were so high the crew couldn't handle them, but rather that you could
(fairly easily) pull the yoke to the stop without it doing much to the
airplane's flight path. You pretty much had to fly the airplane with
the trim, which was why it had dual actuators as well as the backup
handcrank in the cockpit.
To make matters even more fun, there were a couple of conditions
(high-speed dives) where the manual elevator, wimpy though it was as far
as pitching the airplane, could still generate enough force to stall the
trim motors--meaning that the only way to recover was to ease off the
back pressure while holding the trim switch until the motors started
running, then once again fly primarily with trim until back in level
flight. If you ever have a chance to ride in an old 70 (or even
something as a 72), you'll see and hear the trim in motion very
frequently during any speed or configuration changes.
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