I don't like corporate income taxes, and would prefer them to be reduced if not eliminated. I justify this with a desire to also retool marginal income tax rates and taxes on dividends that, while not empirically driven, does a good job conforming to my world view. I'm more than happy to tell you about why I'm pretty sure I'm more right than other people on this if you like.
One interesting aspect of my modification is the implication on capital investments. Currently, firms can write off the depreciation in value of their capital purchases (e.g., computers, trucks, and machinery). This would be eliminated when no taxes are ever paid. The new equilibrium probably has a different bundle with fewer capital inputs - there's less comparative advantage to buying more things.
However, I'm more curious about the implications for economic stimulus. Governments will temporarily grant accelerated depreciation schedules so that firms can write off investments sooner, making the investment 'cheaper' and spurring economic growth. As the Obama Administration continues debating how to give companies breaks that encourage economic development, it would be interesting to see how the discussion changes once you can no longer write off depreciation (because you're not paying taxes in the first place).
Other methods to use tax breaks to induce growth still exist - the biggest being payroll tax reductions. This year, stimulus policy provided the opportunity to avoid payroll taxes on new hires that had been previously unemployed. Making this the only option (since you can't depreciate your capital) means that we can encourage firms to hire, but not necessarily make things. Given the likelihood the government actually goes along with this (none), I say we make Delaware our own personal laboratory for implementing different tax schemes every five years and assessing the impact. If we find a successful formula, awesome. If things go horribly wrong, no worries - nobody cares about Delaware.