As I've explained in previous posts and in comments to previous posts, the federal government doesn't impose a tax to raise revenue per se. It does so to remove dollar financial wealth from the private sector, thereby curbing aggregate demand for goods and services. This dampens inflation and maintains the value of the dollar, which is important for economic stability and growth.
When discussing the efficacy of various tax systems, however, it is easier to speak in terms of tax revenue, and that's what I'll do here.
The vast majority of federal government revenue comes from the personal and corporate income tax. There have been proposals over the years to replace the income tax partially or completely with other types of taxes or revenue raising schemes. Other taxes that have been considered and used at various times and in various jurisdictions include import and/or export tariffs, head taxes, real estate taxes, personal property taxes, intangible property taxes, sales taxes, and value added taxes.
Below, I'll quickly run through the problems with our current tax system, most of which are unique to the income tax:
1) Income is difficult, perhaps impossible to define. Most people would agree that reimbursement for expenses, compensation for damages, money borrowed, return of money lent, return of capital on an equity investment, and de minimus gifts of goods and services should not be considered income for tax purposes. But if you try to craft rigorous rules that tax transfers of items of value between two entities and yet exclude the things that should not be considered income, you find loopholes and unintended consequences everywhere.
2) Because of (1) above, the income tax code is horribly complex and the cost of compliance is outrageous; estimates as high as 5-10% of GDP have been posited for the annual burden/cost of compliance; when one thinks about the brainpower dedicated to finding loopholes in the tax code as well as trying to close them and litigating them, it almost makes one despair.
3) The complexity leads to law-abiding citizens running afoul of the law by accident or because of the malice of government officials; just as damaging, the complexity tempts normally law-abiding citizens to become scofflaws, a slippery slope which probably undermines respect for the law in general;
4) The income tax is necessarily very intrusive; citizens must divulge to the state very personal details about their businesses, their investments, their families, and their spending and giving habits; the income tax strengthens the state vis a vis the individual and makes oppression far more likely;
5) From a purely economic perspective, there can be nothing worse than discouraging work and production, but that's what the income tax does, particularly a progressive income tax;
6) In addition to (5) above, the tax code can also motivate an individual or company to enter into inefficient transactions in order to maximize after-tax income, rather than pre-tax income.
7) The income tax is relatively inefficient because it is very easy to hide income; also, it is hard to predict how much revenue will be raised from an increase in the tax rate because the incentive to hide or shield income (or not to work at all) increases as the tax rate increases.
8) Because of the intrusion of the income tax into all aspects of the economy, it is tempting for lawmakers to use the income tax to encourage socially desirable behavior and discourage socially harmful behavior; as pointed out in (1) above, however, the complexity of taxing income makes the risk of harmful unintended consequences very high.
9) Since the time of the New Deal, taxes have been used to redistribute wealth from rich to poor; whether or not one believes the government should be redistributing wealth, income taxes are a bad way to do it; income -- particularly, taxable income -- is not a good measure of a person's wealth; some rich people have low incomes, and some not so rich people have high incomes; an income tax just taxes those who are the most productive, not those who have the most wealth (a wealth tax would be better), or those who use the most resources (a sales tax would be better).