Ain't no mountain high enough... - what is the tallest LEGO piece?
No restrictions on the materials.


Well then, probably a component to the old wooden furniture LEGO used to produce, like these:

5003483 - 3-Seat Playtable Creative Play Station Center Pack Duplo

Or the similarly designed 4509g - 3-Seat Playtable, 5004063 - 3-Seat Playtable, or 5003468 - 3-Seat Playtable Creative Play Station Center Pack.



IF-LTW2C - Activity Table and Chair Set

 

They did require some assembly, so I'm not sure if any parts stood up on their own, but you could probably balance a table leg for example.