Employers often do quite a bit of research on you before they hire you. Standard background checks are common in some industries, and a genaral search online is almost guaranteed for every job these days.
The first thing most employers are going to do is a quick Google search for your name. They will probably put it in quotation marks. This will likely pull up your social network profiles like Facebook, LinkedIn, Google+ or Twitter, as well as any other mentions of your name online. You want these results to look good. It is essential to make sure that the first results on Google are all positive. Tweaking your social networking profiles is an important part of making you look good and can help push any negative results lower in the list.
Employers can dig deeper if they want and might come across information like Amazon wish lists, campaign donations and more. It might be worth researching yourself before sending off your resume.
Some employers will also do a formal background check. This is a service they usually pay for that takes a few days to complete. Generally, you'll need to provide your name, your last few addresses, and a social security number. From there, the employer will send off that information and get back a list of details about you, including: credit reports, criminal records, certain medical records, bankruptcies, military service, and workers' compensation records. These background checks are typically just to check criminal history.
Your potential employer may also verify your previous salaries, employers, and positions. This process used to require numerous phone calls, but today it is as easy as a quick look online. A majority of employers will verify your resume data, so it is important to be honest on your resume and not to embelish things like salary.
With the Internet today, it is easier than ever for employers to research you, and they're going to do it. Just remember to clean up your social networks and more importantly remember to keep your resume honest.