Are there any truly 'unrecoverable' situations?
One of the more common causes of crash and fatality is a low altitude stall-spin.  A spin, in a modern aircraft, isn't of itself deadly -- with many designs, all you have to do it let go of the controls, and the aircraft will unstall and let you simply fly out of the resulting spiral dive (if you don't wait too long and go past Vne, anyway).

If you get into a stall when low and slow, however, and due to control positions or pilot error initiate a spin, you're likely to hit the ground before you can recover.  Since ground impact in these cases is usually near vertical, nose down, and partially inverted, pilot survival is hardly assured.

Avoiding this kind of fatal mistake is why you practice stalls (with plenty of altitude under you) during flight training -- so you can recognize the conditions that bring on a stall, the aircraft behavior that announces it, and learn how to manage the airplane after the stall occurs to avoid, or intentionally initiate and recover from a spin.

This is (or ought to be) a part of the check ride before flying an unfamiliar type, as well.  Many older designs are less stall friendly than modern (say, post-1960) aircraft -- and if you learned to fly in a Cessna 152, you won't ever have experienced an unintended spin (because the type is difficult to spin even intentionally, and won't do it without large control inputs).  Stall a 1930s light plane at 100 feet, however, and you're likely to fail the "walk away" test.

Another situation that, once in, you can't get out of occurs in mountain flying.  If flying in a canyon under a ceiling (or near your aircraft's ceiling) you may find yourself without room to turn around, but with ground ahead rising into the overcast or faster than your aircraft can climb.  This leads to either "weather" or "Controlled Flight Into Terrain" being the listed cause of the accident, when in both cases it was genuinely pilot error -- this is a situation an aware pilot will avoid.