  The global-in-time existence of bounded weak solutions to general
cross-diffusion systems describing the evolution of $n$ population species is
proved. The equations are considered in a bounded domain with no-flux boundary
conditions. The system possesses a Laplacian structure, which allows for the
derivation of uniform $L^\infty$ bounds, and an entropy structure, which yields
suitable gradient estimates. Because of the boundedness, no growth conditions
for the transition and interaction rates need to be assumed. The existence
proof is based on a fixed-point argument first used by Desvillettes et al.\ and
the Stampacchia truncation method for the approximate system. As a by-product,
the boundedness of weak solutions to population models of
Shigesada-Kawasaki-Teramoto type are deduced for the first time under natural
conditions on the coefficients.
