In addition, they will look into your work history for the last 5 years, and your residences (addresses) for the past 10 years. (You may have to tell them 10 years of employment history, but they only HAVE to verify the last 5.) Be prepared to have all those addresses, numbers, and contacts ready. Call and make sure they are still current- zip codes, too. Don't make it hard for the HR person doing the check.
Some places have asked for a copy of my diploma, or my college transcripts, but I do not know if they called my college.
When they request your records from past airline employers, they are complying with PRIA- Pilot Record Information Act. They will verify your job, dates of employment, training records, and drug/alcohol test results. I think they can ask if you have ever been disciplined- and if you are eligible for rehire, if you were fired etc. But after that, I am not sure. There is a very fine line here- former employers aren't SUPPOSED to talk about you, but sometimes they do.
If you worked at an airline that is now out of business, don't fret. The new airline only has to show they tried to get your records, and that the company is now out of business, so they are unable. However, if you have the number of the Chief Pilot, or some other person that can verify employment, list their name. Might be a good idea to get a copy of your records when you leave a company, so at least you have something if they shut down later. But not a big deal.
Some airlines will do a credit check- they have you fill out a form. Some airlines ask for personal refereces, from people that are not related to you. So have addresses and phone numbers ready. Obviously the family friend that is also a doctor and has known you your whole life is better that the unbalanced roommate freshman year.
Best thing to do is.... pull all your records yourself and make sure you know what they say. Also, when you fill out the PRIA form, you can check a box saying you want copies sent to you, too. You can also hire someone to do a background check on you. Don't assume that the speeding ticket isn't going to show up, or that failed checkride. Be honest.
Keep photo copies of your applications before you mail them in, and bring a copy with you to the interview.
Cheryl Cage or Jackie Boyd books to get some advice on the paperwork.
Good luck!