On the surface, raising the minimum wage would seem to be a good idea. After all, if people are earning more money, they can improve their quality of life. Many people earning minimum wage are also receiving public assistance (food stamps, welfare, etc.), and if their income increases, many of them will no longer need (or qualify for) that assistance.
The problem with raising the minimum wage is that it actually makes some people unemployable. It eliminates some jobs that aren't worth the new minimum wage. The Federal minimum wage is currently $6.55 per hour (as of July 2008, in July 2009 it will increase to $7.25). That means that any job in this country must produce at least $6.55 of value in each hour that is worked in order for a company to break even on labor costs. In order for a company to be profitable, a worker must produce more than their wages in a given hour. If a given worker is producing $7.00 of value for each hour that they work, then that person is profitable for a company. If the minimum wage is suddenly more than $7.00/hour, the company is now loosing money on that worker.
When that happens, the company has a couple of different options. They can raise the price of their goods to make that worker profitable again (this is what most companies do). This means that the small raise the worker just got is offset by the increased cost of goods at the retail level. The company might decide that people just aren't going to pay more for their products, and lay off the workers who are not producing enough value. If these workers are only skilled at one or two jobs, and they aren't providing enough value for what they are paid, they effectively become unemployable. I'm sure if you asked any of these workers which they would prefer, to have their old job back at $6.55/hour or be unemployed, the majority would choose the first option.
As the minimum wage goes higher and higher, more and more people will become unemployable. These people will end up on public assistance, costing more for taxpayers. Goods will become more expensive, impacting everyone (whether making minimum wage or $100,000/year). Employers who pay more than minimum wage will have to give raises due to the increased cost of living, or risk losing their employees to other employers who are paying more. It has a trickle-up effect that is detrimental to the entire economy.
And, it's a snowball effect. As wages increase, business costs increase, which means that consumer prices increase, which means wages need to increase, and the whole cycle starts over. Small businesses are hit the hardest by minimum wage increases, because they often have narrower operating margins. A $1 increase in minimum wage could mean thousands of dollars more in costs for a business over the course of a year. This could be the difference between profitability and failure for many businesses, especially those who aren't in a position to raise prices substantially (such as those in high competition or economically depressed areas).
Overall, minimum wages are ineffective at achieving their goals at best, and detrimental to the overall economy at worst. Increases in the minimum wage are detrimental to all, even those who would seem to benefit (the minimum wage worker).