- A Roomba bumping against a wall.
- A fly buzzing into a screen door or window.
Intelligent but stupid creature (trapped in a slapstick comedy):
- swinging at that fly with a baseball bat, destroying the screen door in the process? (@nitsua60's example from a comment)
i.e. Sees a problem and a solution without considering even some fairly direct consequences.
An "intelligent" creature is smart enough to know it should open a screen door instead of walking into it. And that even if it's lost, walking repeatedly into the (sturdy) wall of a maze won't give a different result the 2nd time.
These examples of "stupid" seem to involve losing sight of the big picture while narrowly focused on one thing. Any Intelligent creature that survives on its own probably always maintains some minimal level of awareness of surroundings, though. Destroying its own house is funny but maybe not realistic, because "don't break my house" is something that a big + strong creature would be used to keeping in mind all the time.
It's also unlikely that you'd see an Intelligent creature run off a cliff while chasing something, unless it's very distracted by an unusual kind of distraction.
@iraserd's example of a Giant throwing a Warhammer at a Fighter is a good one. The consequence is immediate, but only obvious to those who understand what a Fighter can do with their Warhammer.