Not sure what state you're in but I'm in Massachusetts and you're allowed 4 private transactions a year and you have to do the transaction via an E-FA-10 https://mircs.chs.state.ma.us/fa10/action/home?app_context=home&app_action=presentTrans so while there is no " background check " it's still being recorded through the state. If I person shows up and has a valid license to carry that in essence is the background check. Because if he doesn't have a valid LTC then the transaction isn't happening. I have no problem with private transactions,the alternative is to do one through a FFL dealer and they charge anywhere between $20-40 to push a few keys on the computer 
I live in NM.
The following states have no background check required on private sales:
AL, AK, AZ, AR, FL, GA, ID, IN, KS, KY, LA, ME, MA, MS, MO, MT, NV, NH, NM, NC (long guns only), ND, OH, OK, PA (long guns only), SC, SD, TN, TX, UT, VT, VA, WV, WI, WY.
Many of these states, you can literally meet a stranger in a parking lot, and buy/sell a gun, no questions asked. No paper work, no background check. I have purchased and sold firearms this way. I always try to get a bill of sale, with both parties information, DL number, phone number, etc. However, I have run into a few individuals that refuse to do a bill of sale. Usually, there reason for not wanting a bill of sale is, "I don't want a paper trail, that the govt could use to find my guns." Crazy world we live in.