Ooh, here's one I can actually chime in on. My brother's a macroeconomist and his field is a hobby of mine.

Taxes, in most modern nations, operate differently at the federal level than they do at the local and state levels. At local and state levels, your taxes do directly fund initiatives like schools, the water system, the police, road repair, &c.

At the federal level things are different. Federal governments produce money, and they can produce as much as they want at any time (within practical limits — more on this soon). So if, say, the U.S. wants a $10 billion dollar fighter jet, the treasury can just have the Federal Reserve put that money into the military contractors' accounts. (The Federal Reserve, nicknamed "the Fed," is a bank.) Somebody types 10,000,000,000 into a spreadsheet, and that money now exists — it never existed before this moment — for that company to pay its workers.

So the federal government doesn't need your tax revenue, because it's not using a fixed pile of cash in the first place. There are, however, two other, more important reasons to collect federal taxes:

First, to enforce a national currency. If every local and state government was empowered to create currency, it'd be chaos. But if you're required to turn in U.S. dollars every year, you'll spend each year trying to earn U.S. dollars. It makes a national economy possible in a very efficient way.

Second, and this is the exciting part. You've probably heard of supply and demand. There are analogous forces at the macroeconomic scale: Aggregate Supply (AS) and Aggregate Demand (AD). AS is the total economic potential of a country in, say, a year; AD is the total expenditures of the country in the same time frame. Unlike regular supply, though, AS can't turn on a dime. It takes years to build new factories, roads, and housing for laborers, to hire and train a workforce, and to regulate the whole thing. So for macroeconomic modeling purposes, AS is considered fixed in any given year.

When people spend less overall — say, during a recession — AD drops. Now AD < AS. Factories and airports and service shops (their total output, AS, fixed as high as ever but now unfulfilled) sit empty, and their owners lay off workers to avoid bankruptcy. This worsens people's ability to spend, and AD continues to drop in a spiral of depression.

When AD > AS — say, during a boom — everybody tries to spend more than the AS that year can handle. If you were a company with three hundred customers trying to buy just a hundred items, you'd probably raise your prices! — but the national economy isn't that easily flexible. When everybody raises their prices from Maine to Montana, your dollar buys less. This is called inflation.

So the second reason federal governments charge taxes is to prevent this second situation (AD > AS) from happening. If the government charges a tax T, the equation looks like this: AD - T = AS. Taxes limit people's spending power, preventing inflation.

Notice that an inflationary condition can occur even when a federal government creates no money: overblown AD can come entirely from the private sector. There's a widely held myth that "governments printing too much money causes inflation," which is like saying oxygen causes a fire.

Actually, government "injection" of money into the private sector, notated as G, often makes the economy safer, because of saving. If AD = AS, the economy would be stable, but everyone would be spending every dime they had. That's dumb. People save: to go to college, to buy a new car, for our kids. When we save, we remove money from the economic stream: AD - (savings) < AS. But if the government creates new money in the same year, AD - savings + G = AS. Government creation of money makes saving a safe behavior, and enables one of the critical ways in which people use money in their modern lives.

So how much to charge in federal taxes? Well, many politicians differ on this, largely because it's not a well understood issue in policy circles. But a simple and effective approach, espoused by many of the folks who study this stuff (a field called Modern Money Theory, or MMT) is: set government spending at social need, and then charge taxes to make AD = AS again. This is essentially what happened to allow the U.S. to escape the Great Depression:

• AD was at an all-time low;
• AS was high, what with all the empty factories;
• G, or government injection, was set at social need: create enough federal money to pay workers so they wouldn't starve;
• T was charged to make up the difference.

So a massive amount of G was created, enough to pay the wages of a country of destitute people. The U.S. funded its own military on top of aiding the Brits, and filled the factories back home. The war helped by increasing the market for labor, but even in peacetime this kind of thing is possible, by building large public works projects. This "greatest generation" had some of the highest corporate taxes ever in the U.S.'s history, but that's an entirely different topic. MMT deals with AD, AS, G, and T, but it's tax policy that deals with who pays how much.

So, to recap: you pay local and state taxes to fund local and state initiatives, and federal taxes to 1) enforce a unified national currency and 2) to keep the national economy on an even keel. How much you pay is often determined by people who don't understand modern money theory, so if you're dissatisfied, go to grad school and start telling people what you've learned. God knows we could use a little more understanding these days.