CAIN, the Computer Algebra Information Network, providing all kinds of information about Symbolic and Algebraic Computation.
SymbolicNet, Symbolic Mathematical Computation Information Center.
PARI - Package for Number Theory.
KANT for computations in algebraic number fields.
LiDiA, a C++ library for Computational Number Theory.
SIMATH, a computer algebra system, especially for number theoretic purposes.
ZEN, a new toolbox for fast computations in finite extensions of finite rings.
CoCoA commutative algebra system.
David Kohel has several Magma packages for modular and elliptic curves, Cryptosystems and point counting.
THINGS OF INTEREST TO NUMBER THEORISTS
CeNTRe for Number Theory Research, Macquarie University