It seems that I'm in the minority here, but personally I've never really seen what all the fuss is about. Zero is an essential element in place-value numeral systems, and a practical necessity for calculations by hand. But I don't understand the need to read philosophical overtones into what's essentially just clever notation. My pet suspicion is that the fascination speaks to the not-so-rigorous psychology on which math is ultimately based; people have a similar obsession with the concept of infinity.
If you dig a little further back in history, you see that 0 and infinity aren't the only special numbers. Many societies, including my own, have (un)lucky numbers. Numerologists have read meaning into numbers (like the date on which somebody was born) in the same way that astrologers read significance into the stars. The Pythagoreans essentially had a whole religion based on arithmetic and geometry.
Why do humans have such a strong urge to read mysticism into math? I don't have the answer, but I've gotta believe that it's rooted in some psychological fascination with symmetries. Please comment if you have any ideas!