In Alex Kidd in the Enchanted Castle, there is a box-shaped area made of circle blocks in the second level (The Prairie), with an Eagle and Treasure Chest inside:
It's possible to jump down and fly-kick the eagle to get access to the treasure. But here is where I got stuck:
Is there any way out of this mess?
If you're already in the box, there's only two ways out of this mess, and both rely on having won items playing Janken. I've highlighted them on the pause screen:
The Pogo stick can be used to either bounce high enough to escape the trap, or to break the blue blocks beneath:
The cane can be used to airlift yourself out of the hole, although if you don't have another item to use the equip-item glitch, you will consume the use of the cane.
If you realise before breaking the treasure chest, you can stand on top of it to escape. A bit of a contrived scenario, but I suppose if you realise the trap after killing the Eagle but before breaking the treasure chest, you could also use this method to escape.
If you're in the box, have broken the treasure chest, and don't have either of these items, it's effectively a soft-lock. There's no enemies that will come to you and no timer ticking down to (eventually) lose a life. You'll have to reset the game.
It's also technically possible to escape the box using the Pedicopter, but in order to obtain one, you'd have to travel past this box, all the way to the end of the level, complete the Janken challenge there to win one, then travel all the way back to the box. Impractical for this application, considering point 4:
Of course, if you know this box is a trap beforehand, and don't have any of the aforementioned items, you can also break some of the blue blocks from below, allowing you to leave the box after collecting the treasure:
As far as I recall, if you get a running start, you can gain an additional block when you jump. I believe this is just high enough for you to be able to get out. :)
