We find new classes of {\it exact} string solutions in a variety of curved
backgrounds. They include stationary and dynamical (open, closed, straight,
finitely and infinitely long) strings as well as {\it multi-string} solutions,
in terms of elliptic functions. The physical properties, string length, energy
and pressure are computed and analyzed. In anti de Sitter spacetime, the
solutions describe an {\it infinite} number of infinitely long stationary
strings of equal energy but different pressures. In de Sitter spacetime,
outside the horizon, they describe infinitely many {\it dynamical} strings
infalling non-radially, scattering at the horizon and going back to spatial
infinity in different directions. For special values of the constants of
motion, there are families of solutions with {\it selected finite} numbers of
different and independent strings. In black hole spacetimes (without
cosmological constant), {\it no} multi-string solutions are found. In the
Schwarzschild black hole, inside the horizon, we find one straight string
infalling non-radially, with {\it indefinetely} growing size, into the