An interesting problem to ask students to think about is this: Write down a definition of 'left' (as in the opposite of right). It's something every adult knows, but how do you define it. There's little wonder that children take a long time to grasp which is left and which is right.
One might say: Well, if you are in the Southern Hemisphere, face the position of the midday sun and left will be the side of you where the sun sets. But that just shifts the problem to another: Define 'south'. Then one could resort to physics, and look at the direction that a positive particle is bent under a particularly oriented magnetic field, but that muddies things further - we need to know about positive and negative and also left and right - so we are no better off.
In order to do it, you need some asymmetry in the universe. Fortunately, there are some we can draw from. For a start, the Earth isn't symmetric - just by saying 'in New Zealand' we establish ourselves as being in the southern hemisphere, then we can apply arguments about where the sun sets etc.
There are also other asymmetries. There is more matter than antimatter, for example. Why? It's something that the Large Hadron Collider might give some clues about (It wasn't built just to find the Higgs Boson). There are more subtle ones, concerning CP-violation in particle physics (this actually links back to the matter/anti-matter asymmetry) which suggests that there is a fundamental asymmetry about the universe. But why?
What got me thinking about this was the clockwise rotation of baby Benjamin at the weekend. Lying on the in-laws living room carpet, he seemed to be quite able to rotate clockwise (so that his head swizzled round roughly to where is feet were) but not anti-clockwise. So there is a preferred direction. It could be because one leg is stronger than the other, which is quite possible, but there may be other reasons - for example the 'grain' in the carpet might be an issue here.
One thing's for sure - he's living in an asymmetric universe.
Postscript 22 November 2012
This news has just come out: An experimental measurement of time-reversal symmetry breaking. That's allowed by our current physics understanding - what isn't allowed is charge-parity-time reversal (CPT) symmetry violation.