I love the way it crumples when I smash my way out of it.
I have to start by saying that Nesh's advice is absolutely spot on. You have to know the box before you can climb out of it.
But once you've done that... I recommend thinking about things you've read, and what approaches (not solutions, approaches) they used that you enjoyed.
One that I like to see is using the question of who knows what, and in particular applying this to weaknesses or differences in the hero's resources. (Example: On Basilisk Station, by David Weber, features a starship with a highly unorthodox - and mostly useless - weapons loadout) To craft an example, let's say our protagonist is a wizard in a world where the only spell is Fireball. Trouble is, our wizard is self-taught: she's just as powerful as the villain, but rather than being able to fire big balls of fire, she's limited to little ones. However, she can put out a lot of them - she's kind of a fireball machine gun.
So, what if the villain doesn't know this? He sees her small fireballs, but assumes she's just a weak magician who can't make anything bigger. Of course, she might be trying to trick him, so he sets up defences on the assumption that she can make a fireball as big as his - but he doesn't account for the 'machine-gun mage' scenario, because it's never occurred to him.
A second approach I enjoy is drawing contrast between what people treat as the limits of their resources, and the actual limits, which are usually the laws of physics. (Example: One of the Codex Alera books, by Jim Butcher, features the unexpected weaponisation of the freeze-thaw cycle.) Coming back to our wizard: she can't make a fireball big enough to burn into the fortress, but what else do fireballs do? Well, they emit light - so you can blind your enemy without going anywhere near him. They also impart kinetic energy when they hit, so you can knock things over. There's even a Star Wars novel which freezes a planet by shooting it (and kicking off a runaway evaporation cycle), so that's a possibility too. None of which the villain will think of.
A third idea is the classic Just Shoot Voldemort concept, where you change the rules by introducing a different type of technology. This doesn't have to be something new and powerful - just something unexpected. (Example: Sourcery, by Terry Pratchett, takes out the world's most powerful wizard with a half-brick in a sock. Sort of.) Coming back to our wizard, is the villain expecting a magical duel? If so, how about poisoning his wells instead? Or just sneaking in and stabbing him. Anything other than using what he expects you to use.
The original PPC, with its agents who are deliberately much weaker than their enemies, was a masterpiece of this. Consider the mission where Jay and Acacia take out the Suvian with a ball of invisible yarn - that example uses all three of the concepts I've just described, and it works really well for it.
hS