What is the tallest Jenga tower ever created?
According the the 2008 Vintage Game Collection version of Jenga, the tallest recorded Jenga tower was made by Robert Grebler in 1985 with a tower 40 2⁄3 levels*, using an original Jenga set produced by Leslie Scott, the designer of the game. 

Board Game Geek's gallery for Jenga includes a picture that nearly matches this at 40 levels tall. The user Romir posted a picture of a tower 43 levels tall, but it looks like they didn't follow the rule to complete a 3 block story before starting another one.**



For fun, there is a YouTube video of the Tallest Game of Jenga Ever Assembled at 66 inches (5.5 feet, 1.68 meters), using multiple sets.

* Presumably, the "2/3 levels" means that the Robert Grebler placed 2 out of a possible 3 blocks on the top level before the tower collapsed. In Jenga, you must place three blocks on a level before starting a new level.

** As described above, a level must have three blocks on it before starting another level. Therefore, it's not possible for both the top level and the one below it to only have one block, as shown in the picture.