Babysitting taxes falls into the same category as lawn mowing taxes, or house cleaning taxes, or any other job that isn't regulated by a company that reports directly to the IRS. In other words, you have to do it yourself. Don't fall into a trap by not filing. There are specific rules for how much you make and what your claim status is. And of course, if babysitting is your main source of income, it is a given that you'll need to file.
The most "official" place to start is the IRS page. Babysitting taxes are handled the same as contractor taxes, so depending on how much you make each year per family, you may need to fill out a W9 form for the parents. Another interesting site with good information especially for teens running businesses is the Teens Business Forum. It addresses the babysitting issue but offers much more by way of starting and running a business.
eHow's article on how to claim babysitting on income taxes is straightforward with instructions on what tax forms you'll need and how to fill out each line of your forms.
If you're not the type of person who enjoys working on taxes by yourself, try The Nanny Tax Company, which is dedicated to the profession of child care.
Babysitting and Nanny taxes certainly fall into the same category; the difference is that nannies are considered professionals at the field, where a babysitter may be someone who is part-time or who has another profession as a career.
Livestrong has an info-rich page on filing taxes for babysitting, along with helpful links and a blog format, which allows for comments and questions.
More than likely, you'll make enough money to warrant filing taxes, and the parents or guardians whose children you sit will appreciate your responsibility and cognizance of tax laws. If you own a babysitting business, that's when many items are deductible, so make sure you take advantage of them. And always make sure to discuss with long-term babysitting jobs whether the parents/guardians plan on claiming you on their tax forms.