^^Self weight
is the gist of Troubadour's question.
Lets take a 1x1 brick for a simple example.
http://www.clear.rice.edu/elec201/Book/legos.html
Measuring a brick myself, it looks like the walls of each brick are 1.5 mm thick.
That gives a cross section for a 1x1 brick of 8mm x 8mm - 5mm x5mm, or 39mm^2.
9000 psi converts to 6.33kg/mm^2.
39mm^2 x 6.33kg/mm^2=267kg that a 1x1 brick can support.
267kg/.00000108kg/mm^3 =228,600,000mm^3
Approximating the stack of bricks as a hollow column,
228,600,000mm^3/39mm^2=5,860,000mm=5.86km high stack.
As others have noted, this figure will be further limited by other considerations such as buckling and overturning. Unfortunately, I'm too tired to consider them right now.