I like it when a hero winds up shipwrecked on a beach, or enslaved in a mine, or imprisoned, or otherwise brought into great trouble with no equipment on them save their wits, always ready to grab a new sword - or make one of their own - and go out there swinging it and taking names. This happens to Conan a fair bit, for instance. Or Lara Croft about once in each of the games I actually played.
But it is a bit of a problem in that my own heroes tend to be heavily tied on a few items of great magical or historical value. Being unable to get rid of these things in any lasting and meaningful way locks out a great few stories for them. I've written myself into a corner, a bit.
Then again, even as I've now begun thinking about it, I'm already coming up with solutions. So that's nice.