As mentioned above, many packages can do this job. (Biopython, Bioperl , Biojava, Bio3D, MMTK, Pymol, VMD, Chimera, YASARA, etc., ) and - the popular secondary structure calculation tools namely DSSP & Stride outputs phi/psi angles.
There is also a well established, fast code written in C, called as torsions.c from : http://www.bioinf.org.uk/software/torsions/
Another good program called Dangle , a java-code also provides this along with the other torsion angles including side chain torsions (chi1, chi2, chi3 etc., ) - this is from Richardson's lab who has created MolProbity (that extensively checks the goodness of a protein structure based on allowed regions in Ramachandran space & clashes etc., ) http://kinemage.biochem.duke.edu/software/dangle.help.html
PRODY , a very good package developed in the past 2-3 years (since the previous posting & answers) also does this phi/psi calculation well. http://prody.csb.pitt.edu/
Another tool, part of the pdb-tools package available on Google Code, also has a pyton script for this calculation !