A lot of people blame Banach-Tarski on the axiom of choice. I disagree. I think it's in essence just a variant of the Hilbert hotel, with the axiom of choice merely serving as part of the machinery for this manifestation. In other words, it's just a counterintuitive but true consequence of the nature of infinity. As such, I think any mathematical system that acknowledges infinity, is going to have such counterintuitive results.