As I understand it if you're a licensed gun dealer you must do a background check at a gun show.
If you're "private" though, nope.
That's a pretty damn big loophole.
Actually it depends on the state, I pulled this from Snopes:
Though commonly referred to as the “Gun Show Loophole,” the “private sales” described above include guns sold at gun shows, through classified newspaper ads, the Internet, and between individuals virtually anywhere.
Unfortunately, only six states (CA, CO, IL, NY, OR, RI) require universal background checks on all firearm sales at gun shows. Three more states (CT, MD, PA) require background checks on all handgun sales made at gun shows. Seven other states (HI, IA, MA, MI, NJ, NC, NE) require purchasers to obtain a permit and undergo a background check before buying a handgun. Florida allows its counties to regulate gun shows by requiring background checks on all firearms purchases at these events. 33 states have taken no action whatsoever to close the Gun Show Loophole.