According to Wikipedia:
Many clocks use a 32.768KHz crystal. Is this because the crystal is smaller than a 1Hz crystal?
If 1.0 Hz == 1.0 second. Then, why the need for the division?
The main reason is that a 1 Hz crystal would have to be physically very big. A crystal is a piece of quartz that mechanically vibrates at the specific frequency. Since quarts exhibits a fairly strong piezo-electric effect, those vibrations also cause electrical signals and vice versa.
Getting a physically small crystal down to 33 kHz resonant frequency was quite a breakthru not that long ago. The trick is to shape the quartz like a tuning fork. That allows for much slower oscillations than a solid block of quartz of the same size. However, extending that another 3½ orders of magnitude is going to make the crystal a lot bigger.
It's hard to imagine what use a 1 Hz crystal would be, considering how cheap and easy it is to start with a faster frequency and then divide down with a counter. 33 kHz is already so slow that you won't get any significant power savings by running the logic any slower. In fact, filtering the harmonics from a 1 Hz square wave and still providing the drive for the size crystal that it would take to make that frequency would take significantly more power. It just doesn't make sense. Put another way, a 33 kHz crystal with its drive circuit and a digital counter is smaller, cheaper, and takes less power than a 1 Hz crystal with the drive circuitry it would require.
Aside from the practical aspects of making a 1 Hz crystal, every crystal is going to have some degree of jitter. If you have a 1Hz crystal to generate 1 second ticks, every bit of that jitter manifests as error in your clock. If you start with a higher frequency and divide down, that error gets minimized.
For example, a 1Hz crystal with 1% jitter would give you 1 sec +/- 1% ticks. A 1kHz clock with 1% jitter going through three divide by 10 chips will give you 1 sec +/- 0.001 % ticks.
EDIT: http://www.silabs.com/Support%20Documents/TechnicalDocs/Clock-Division-WP.pdf shows a great discussion on this. Look particularly at the phase noise reduction as division increases in figure 6, and the following table, which shows the jitter expressed in time as staying constant.
Most of life's "physicality" isn't going to affect a 32k xtal. We live physically in the low tens of Hz maximum (except hearing) and a 1Hz xtal is gonna come in for a few resonant bumps. Given also that it's nearly a qtr of a mile long (according to Brian Drummond) settles the argument for me.
OK maybe bats can disturb a 32k xtal?
There is also the problem with drift, due to environmental issues. From wiki:
A crystal's frequency characteristic depends on the shape or 'cut' of the crystal. A tuning fork crystal is usually cut such that its frequency over temperature is a parabolic curve centered around 25 °C. This means that a tuning fork crystal oscillator will resonate close to its target frequency at room temperature, but will slow down when the temperature either increases or decreases from room temperature. A common parabolic coefficient for a 32 kHz tuning fork crystal is −0.04 ppm/°C².
In a real application, this means that a clock built using a regular 32 kHz tuning fork crystal will keep good time at room temperature, lose 2 minutes per year at 10 degrees Celsius above (or below) room temperature and lose 8 minutes per year at 20 degrees Celsius above (or below) room temperature due to the quartz crystal.
In practical terms, a 1Hz crystal will mean that the slightest change in temperature, will cause the clock to be fast or slow by minutes per day, instead of nanoseconds. Over a year, that would make it one of the most inaccurate clocks ever, without daily adjustment.
And that is just temperature. Pressure (And Altitude), Humidity, and vibration also come into play. So unless the crystal is in a a completely controlled environment, it is simply impractical for common everyday time keeping use.
There are 1Hz oscillators, only they are made using MEMS tech (bye quartz).