The
Chick-Fil-A drive-thru in Springfield, Virginia, is notorious for that, although Street View doesn't show it backed up all the way out onto Backlick Road. In the image, you can see the restaurant itself to the far left near Advance Auto Parts (the drive-thru exit is between Advance and Chick-Fil-A), and the drive-thru entrance is straight ahead of the camera viewpoint (the SUV and the Camry coming from the right are most likely part of the drive-thru line). Several businesses have left that shopping center, and others have expressed an intent to leave, because the drive-thru line so severely interferes with parking.
The Raising Cane's in Charlottesville has been noted to cause traffic problems on US-29, though no Street View imagery of a backup there is available.
In a similar situation that doesn't involve a restaurant, the Mr. Wash Express car wash at the corner of Edsall Road and Van Dorn Street in Alexandria, Virginia, sometimes backs up so much (despite having two queues) that the city police wind up coming out to try to manage the congestion since it's adjacent to an intersection. Arguably too small a piece of property for a place that's so busy.
Finally, while this one doesn't back up out onto the street, it can be almost as bad in some respects:
The drive-thru for the KFC/Taco Bell here in Kingstowne always backs up and often blocks access to the other drive-thru for the Burger King located in the same row of stores (see the blue SUV located in the distance beyond the silver Chevy SUV). Drivers can't seem to agree on how to form the drive-thru line when it backs up to, or beyond, the point seen in this Street View image. They've started work to put in a Chick-Fil-A
in the same shopping center where the Irish pub used to be. I don't necessarily think the traffic waiting for the drive-thru will be a huge problem, but I think the traffic
exiting from the drive-thru is going to cause major problems because the shopping center's exits are poorly-designed. Good thing it's close enough that I'll be able to walk there for my chicken fix.