Great "constants" of economics
One of the original statements of this kind were Kaldor's Stylized Facts on growth, Kaldor's Facts, the most important of which are that:


Labor and capital receive approximately constant share of output (about 0.6 for labor and 0.4 for capital)
The rate of growth of output per worker is roughly constant (about 2%)
The rate of return on investment is roughly constant (if you look at long enough intervals, i.e. about 3%...)


More recently, the famous growth theorist Paul Romer came up with a renewed set of facts New Kaldor Facts paper. The most salient ones are that:


Market is constantly increasing its dominance as a way to organize economic activity.
The rate of economic growth has been accelerating for millenia. 
Measured inputs explain only a small part of income differences across countries.
Human capital is constantly being accumulated, and yet, the human capital premia has not changed over time.


Also, a newly minted constant, as theorized by Minsky:


The nature of financial markets and risk taking implies periodic financial crisis.