To start this off, I'll show one from DKC and one from DKC2.
Get stuck in Snow Barrel Blast, DKC:
Enter the second bonus area (via the bonus barrel pictured in the first snapshot below), which is just a little past the midway point. Leave the bonus, and return to where you entered it from. The barrel is no longer there (this is common to DKC's bonus barrels, they disappear after use), and so there is no way to get back up!
Well okay, there is- but it's rather an extreme measure. (see below)
How to continue: If you have both Kongs (easy, courtesy of the nearby DK barrel), jump and hit the Zinger floating around nearby (pictured above, third snap). DK reaches higher, so use him. Now guide Diddy (or DK, if you did it the hard way) into the nearby barrel cannon, and voila! Of course, if you get hit, and fall back down after having broken the DK barrel... You are completely stuck!
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Get stuck in Arctic Abyss, DKC2:
The changing water levels in some of DKC2's levels make gameplay very interesting... but they can also lead to unpleasant scenarios! It's possible for Enguarde to get himself stuck with a few quick thrusts in the reverse direction at the spot seen below. (again, just after midway)
You can still explore all of the areas you've been to previously in the level (you can even take on Kaboom as Enguarde, if you like!), but are unable to continue further ahead.
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Alright guys, this is for DKC, DKC2 and DKC3 inescapable situations, or situations which require extreme measures (such as dying) to continue from. No, getting into an imminent-death situation and pausing the game doesn't count! I'll accept glitches which make the level unable to be completed, but not ones that just freeze the game completely. If you want to post DKL, DKC port or DK64 inescapable situations, that's okay here, too. Although if I see more than two or so for any one of these, we'll have to start a similar thread in the appropriate spot.
Got any other 'inescapable situations' worth sharing?