Jay Porter sums it up in Slate:
Studies have shown that tipping is not an effective incentive for performance in servers. It also creates an environment in which people of color, young people, old people, women, and foreigners tend to get worse service than white males. In a tip-based system, nonwhite servers make less than their white peers for equal work. Consider also the power imbalance between tippers, who are typically male, and servers, 70 percent of whom are female, and consider that the restaurant industry generates five times the average number of sexual harassment claims per worker. And that in many instances employers have allegedly misused tip credits, which let owners pay servers less than minimum wage if tipping makes up the difference.
Porter's not just speaking abstractly. He ran a restaurant where he abolished tipping. The result, he writes, was that the food improved, the service improved, and everyone made more money. Here's more on the subject from Slate's Brian Palmer.
Now, if you're not having customers pay waiters in tips, you have to actually pay them real salaries. This might sound shocking, but as Porter notes, it's the norm in pretty much every other profession, and it seems to work pretty well.