Signs.com asked dozens of Americans to draw the logos of well-known companies from memory, including Domino's, Apple, Adidas, and Starbucks. As you can see, there was a wide range in aptitude and some logos fared better than others; overall the Starbucks and Foot Locker logos were the worst drawn while Ikea and Target were the best represented.
There is also this (a true story):
Adidas, the second largest sportswear company in the world, acquired its three-stripes logo in 1952 from footwear brand Karhu Sports for two bottles of whiskey and the equivalent of $2,000.
See also drawing all 50 states from memory, can you draw a working bicycle from memory?, and maps drawn from memory.