I always thought the answer was no, you can never balance an egg; but snopes.com, a site that debunks old wives tales like alligators coming out of your toilet or keeping batteries in the freezer to extend their life, says this:
The Chinese are thought to have originated the practice of standing eggs on end during the equinox. Just as the equinox symbolically restores balance to the world by signalling its rebirth after a season of darkness, the equinox literally balances the day by dividing it into equal portions of darkness and light. If the symbol of fertility, eggs, could be balanced on end during a day equally divided between day and night, this was a sign that all nature was in harmony.
Nonetheless, the vernal equinox brings no special egg-balancing properties with it. Standing an egg on its end is something just about anyone can do any day of the year; the feat simply takes the right egg and a little trial and practice.
In my bad feng shui room over the garage as I was growing up I had pink curtains, and one year I got the idea to close them on the winter solstice and not open them again until spring officially arrived (always celebrating time, I was, albeit in a slightly depressing way back then).
Hence the pink (though check out the Google doodle today – it’s what I would do if I knew how to do such things). Happy Spring.