Once upon a time, I was an engineer with only the most superficial understanding of taxes and the economy. Today, I'm still only an engineer (at heart), but in the many many years of working and investing I've learned a few things. (I have only had one formal course in economics. At least it was taught by Robert Solow.) Those that already understand the corporate tax even a little should probably skip this post (and to those that really understand it feel free to correct me where I don't understand it well enough). Taxes and their effects are considerably more complex in real life than my examples below.

When a partnership makes money, the profits flow through to the partners and are taxed as ordinary income, so to compare:

XYZ Parners (having 10 equal parners) makes $10,000,000
Tom (a parner) has:
Additional ordinary income: $1,000,000
Taxes:
Federal (%39.6) -$396,000
State (CA %12.3) -$123,000
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Net: $481,000

ABC Corp (with say 10 owners) makes $10,000,000 in profit
Corporate profits $10,000,000
Taxes:
Federal (%35) -$3,500,000
State (CA %8.84) -$ 884,000
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Net: $ 5,616,000

Note that this $5,616,000 can be retained by the corporation, but nobody actually benefits from it until it is distributed to the owners, distributed to it ten owners as dividends:

Tina (an owner) receives $561,600 dividend payment
Additional investment income of $561,600
Taxes:
Federal (%23.8) -$133,661
State (CA %8.84) -$ 49,645
----------------------------------------------------
Net: $378,294

There are a few things to notice here, before an owner gets any money out of a C corp, there are four taxes leveied and over %60 of the company's profits are taxed away. This puts corporations at a disadvantage, tax-wise, to parnerships under my very simplified example. They are also at a disadvantage to foriegn corporations that don't have high corporate tax rates.

There are direct ways for the corporation to control its profits. It can increase wages to employees. In this case say there are 100 employees, each compensated the same and all profits are paid out to employees:

Tim (an employee) receives a bonus of $100,000 (1/100 * 10 Million)
Additional ordinary income $100,000
Taxes:
Federal (%35) -$35,000
State (CA %8.84) -$ 8,840
---------------------------------------------
Net: $56,160

These taxes are paid by each of the 100 employees receiving bonuses.

Another way that a corporation can lower its profits is by lowering the price of good sold, which benefits consumers.

Owners of the corporation like Tina above want to make something from the ownership of the company and through the board of directors (voted in by Tina and the others) they expect the company to eventually issue dividends (even if it is too far in the future to benifit Tina the building retained earnings will drive up the value of Tina's shares because of the anticipation of future dividends). This keeps corporations aiming for profits; their owners insist on it. Eventually Tina will have to pay taxes on the capital gains from the increased value of her shares or to pay taxes on dividend issued by the corporation.

Note that parnerships don't pay corporate taxes, instead the owners pay income taxes on the profits. Corporate taxes introduce another layer of taxes and complicate the tax system. Why not have zero corporate tax? Firms structured as parnerships don't pay corporate taxes and the income will still be taxed by the time it gets to Tom or Tina. No indivdual gets away without paying taxes on money he or she receives no matter what the corporate tax rate is. This is why other countries can have lower corporate tax rate that the US.

Of what benefit are corporate taxes. Like VATs, corporate taxes affect the entire population. The impacts are diffuse and a bit opaque so the voters being affected by it are unaware of it, so it is a less painful way for governments to raise more revenue from us. Corporate taxes raise the cost of capital to corporations, which has a negative impact on the growth of the overall economy. Further, it incentivises companies to actively lobby for special breaks and perks. Politicians of all stripes like this system because corporations are big donors that keep the croney capitalism going.

The real question is who bears the corporate tax and is this the most efficient and fair way to collect taxes [1]. In my own opinion, I don't think it is a good idea. Why not simply raise taxes on dividend income to ordinary rates and eliminate the corporate tax entirely. This would eliminate the competition for loopholes that distort the whole economy and hurt us all.

[1] Who Bears the Corporate Tax? A Review of What We Know, http://www.nber.org/chapters/c0065.pdf