A cashless exercise usually means that all options are exercised & the broker sells just enough shares to cover the ISO stock basis & mandatory tax payments. If your ISO price were $1/share & you exercised 1,000 options, you'd need to pay $1,000 for the stock. The broker would sell $1,000 worth of stock, but you'd continue to own the remainder.
The advantage of the cashless exercise is that you avoid a huge regular tax hit. Your income is only the $1,000 from the stock sale. This income shows up in your W-2 as wages & is subject to the regular payroll taxes. The unsold shares are not taxed. Also, if you hold any shares for more than a year, when you sell, those shares generate capital gain/loss. This means you avoid paying ordinary income tax rates & don't have to pay social security/medicare taxes on the gain.
The disadvantage is that you might trigger AMT liability. Without knowing your specific circumstances, we can't make any guess as to whether you'd face a big AMT tax hit or not from exercising the options & holding them.
I strongly suggest you consult a financial advisor and/or tax pro with experience handling ISOs. You may end up waiting until January to exercise the options, selling the minimum, or you may exercise & sell all ISOs, in which case it may be better to do it in 2007.