  For a generic quantum field theory we study the role played by the
renormalization-group (RG) running of the cosmological constant (CC) in
determining the ultimate fate of the universe. We consider the running of the
CC of generic origin (the vacuum energy of quantum fields and the potential
energy of classical fields), with the RG scale proportional to the (total
energy density$\rm{)^{1/4}}$ as the most obvious identification. Starting from
the present-era values for cosmological parameters we demonstrate how the
running can easily provide a negative cosmological constant, thereby changing
the fate of the universe, at the same time rendering compatibility with
critical string theory. We also briefly discuss the recent past in our
scenario.
