Typically, as the market rises the VIX drops and visa versa. A more ambiguious relationship is the relationship between the volatility of volatility and the market.
Here are some observations I stumbled across (as of roughly 1:30 9/15/11).
Implied volatility from the cost of VIX options is now more than double historic volatility based on the past 30 days. Because the implied volatility of the VIX is still relatively high, the observed gap is probably mostly based on how unprecedented the types of moves in volatility we saw in August. For calculated volatility to continue to stay at this level, the broad market would need to make an even less precedented move than the one we saw in August. The head-scratchingly cheap volatility observed leading into the measured period - in July, the VIX closed below 20 on 13/20 trading days - set the stage for this explosion in calculated volatility of volatility, so we should not expect VIX option premiums to be at this level. Nevertheless, a ~60% option premium discount is something worth mentioning, and maybe suggests we aren't headed for a complete market meltdown.
To get a better idea of what exactly was going on here, I looked at the VIX option chains for October 2011, and January 2012. Here are the observations:
(Click charts to expand)
October VIX calls at a slight premium against an implied volatility of 94%.
October VIX puts at a slight discount against an implied volatility of 94%. October chain would suggest a slightly bearish tilt in the broad market - if the VIX is rising generally the market is selling.
January calls and puts both at discounts to 94% implied volatility. Tough to read too much into this because you cannot exercise VIX options before maturity. You can, however, sell them back to the market. In some situations VIX options actually carry a negative time premium based on the contagion and backwardation of futures prices, which makes pricing them even more complicated. The one assuring sign from the January chain is that the put discounts are significantly less than the call discounts - implying a lower VIX close in January is more likely than a higher - which would indicate sentiment toward a more stable market by their expiration in January as opposed to prolonged very high volatility.
As purely a speculative idea - if the VIX were to close at or below 20 in January (like it did this January after the summer calamity) buying a far out-of-the money VIX put could be extremely profitable (300%+), and based on current implied volatility, would be purchased at a huge discount. It could even serve as a great hedge for those of you who are net short.
Clearly these chains are open to interpretation, and I'd really like to hear others' perspective on this rarely discussed issue.