Modulef - Modular finite element library. - http://www-rocq.inria.fr/modulef/english.html
MODEL - Finite element code by Professor Ed Akin. - http://www.owlnet.rice.edu/~mech517/
GeoFEM - Written primarily in Fortran 90 and MPI. Parallel finite element codes for linear/nonlinear solid mechanics and thermal fluid simulations, parallel iterative linear solver library, partitioning subsystem, parallel visualization subsystem and utilities for - http://geofem.tokyo.rist.or.jp
Finite Element Analysis Program (FEAP) - General purpose finite element analysis program which is designed for research and educational use. Source code of the full program is available for compilation using Windows (Compaq or Intel compiler), Linux or UNIX operating systems, and Mac OS X based - http://www.ce.berkeley.edu/~rlt/feap/
ADINA for Universities - Accompanies book "Finite Element Procedures" by K. J. Bathe. - http://www.adina.com/educ.shtml
MultiGrid Galerkin Hierarchical Adaptive Triangles (MGGHAT) - Solve second order two dimensional elliptic partial differential equations, using adaptive refinement of second, third, or fourth order elements, and multigrid solution techniques. - http://math.nist.gov/~WMitchell/mgghat/mgghat.html
Diablo95 - Parallel finite element simulations in Fortran 95. - http://diablo95.sourceforge.net/