When and why did tipping become such a common custom in the United States?

Tipping was a European custom in the late 1700s / early 1800s and was used to gain favor and ensure a better service. Affluent American's would visit Europe and brought back the custom, most likely, to look powerful and trendy. In the early 1900s there was a breaking point between the rising culture of tipping and the opposition of the idea, with the tip ultimately surviving.

edit: for more specific history here is source http://ideas.repec.org/p/wpa/wuwpeh/0309001.html

Thats pretty much the basic history of the tip in America. I don't think it gets interesting until the government stopped scaling tip based salaries with inflation. I wrote a paper on tipping in America about two years ago so the sources and specifics arent very fresh....

Prior to the Small Business Job Protection Act of 1996 minimum wage for tipped employees was set at 50% of minimum wage, which was regulated by the Fair Labor Standards Act (FLSA). So in 1996 the FLSA set the minimum wage to 5.15 but the SBJPA set tipped wages to the current 2.13. You'll notice that the cost of eating at places with tipped wage servers has risen sharply while they aren't paying employees more and we are expected to pay 15-20% in tips.

I dunno if this answer will count for anything but there really are a lot of resources available on the subject if you are willing to do a small amount of research.

Edit: It is worth noting that states have their own minimum wage laws that trump federal law as long as the state minimum wage isn't below the federal level.