> Why doesn't the Fed just lend this money to ordinary people and businesses directly at 0% interest?

Good question. Two questions, actually: why doesn't the central bank lend to individuals, and why can't individuals get the same interest rate on loans as a bank.

One reason you and I can't get loans at the prime rate (normally in the 2-5% range) is because we don't have the same creditworthiness as a bank. I don't know about you, but I don't have hundreds of millions of dollars of assets like banks do.

(A decade or two ago, when banking was a more boring and staid business, the creditworthiness of a bank was virtually never in question. In comparison, individuals go bankrupt all time. Granted, there have been periods of banking abuse-- the S&L scandal, the over-leveraging in the 2000s, etc-- and one can rightly criticize the banks in those contexts. In fact, lots of people think that banking should return to the lower-risk model of banking, where banks are more deserving of their credit. But back to your questions.)

Why doesn't the Fed lend to individuals? The Fed's mission is to set fiscal policy. From
http://www.federalreserve.gov/pf/pf.htm, "Goals of Monetary Policy":

The goals of monetary policy are spelled out in the Federal Reserve Act, which specifies that the Board of Governors and the Federal Open Market Committee should seek "to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates." Stable prices in the long run are a precondition for maximum sustainable output growth and employment as well as moderate long-term interest rates. When prices are stable and believed likely to remain so, the prices of goods, services, materials, and labor are undistorted by inflation and serve as clearer signals and guides to the efficient allocation of resources and thus contribute to higher standards of living. Moreover, stable prices foster saving and capital formation, because when the risk of erosion of asset values resulting from inflation - and the need to guard against such losses - are minimized, households are encouraged to save more and businesses are encouraged to invest more.

So you see, the intent of this modern economic tool, control of the money supply, is to promote stability while maximizing output. You said:

If we are going to have such a system whereby the Fed must print money, which means that the money in the system looses value...

Actually, printing money doesn't necessarily mean that existing money loses value. The Fed attempts to expand the money supply as the economy grows to maintain the current value of money. If it the money supply were suddenly static while the economy continued to grow, I believe this would result in a deflationary spiral: the first stage is where the expanding value of the whole economy must be denominated by a fixed pool of money, causing the value of that money to increase-- which sounds nice at first. But deflation reduces incentives toward spending and lending, and ultimately curbs growth-- which is bad. So if the size of the economy were fixed, then perhaps a fixed money supply would be desirable. Fortunately, the global economy, in the long term, is growing; so the money supply must grow as well. This reaches the limits of my memory of basic macroeconomics from my B.A. in the late 90s. I'm a programmer; this stuff isn't top of mind, so I'm sure an actual economist could provide better explanations of several of the points above. But I think it's generally accurate.